Braga, Rodrigo O.; Del-Vecchio, Renata R.; Rodrigues, Virgínia M. Integral unicyclic graphs. (English) Zbl 07312135 Linear Algebra Appl. 614, 281-300 (2021). MSC: 05C50 15A18 05B05 PDF BibTeX XML Cite \textit{R. O. Braga} et al., Linear Algebra Appl. 614, 281--300 (2021; Zbl 07312135) Full Text: DOI
Noubissie, Armand; Togbé, Alain On some ternary Diophantine equations of signature \((p,p,k)\). (English) Zbl 07311090 Bull. Malays. Math. Sci. Soc. (2) 44, No. 1, 163-170 (2021). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{A. Noubissie} and \textit{A. Togbé}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 1, 163--170 (2021; Zbl 07311090) Full Text: DOI
Dieulefait, Luis; Soto, Eduardo Solving \(a x^p + b y^p = c z^p\) with \(abc\) containing an arbitrary number of prime factors. (English) Zbl 07302848 Mediterr. J. Math. 18, No. 2, Paper No. 48, 24 p. (2021). MSC: 11D41 11F33 11F80 11G05 11D61 11R18 PDF BibTeX XML Cite \textit{L. Dieulefait} and \textit{E. Soto}, Mediterr. J. Math. 18, No. 2, Paper No. 48, 24 p. (2021; Zbl 07302848) Full Text: DOI
Bennett, Michael A. Integers represented by \(x^4 - y^4\) revisited. (English) Zbl 07302533 Bull. Aust. Math. Soc. 103, No. 1, 38-49 (2021). MSC: 11D41 11F33 11F80 11G05 PDF BibTeX XML Cite \textit{M. A. Bennett}, Bull. Aust. Math. Soc. 103, No. 1, 38--49 (2021; Zbl 07302533) Full Text: DOI
Guzman, Patricio; Rosier, Lionel Null controllability of the structurally damped wave equation on the two-dimensional torus. (English) Zbl 07299441 SIAM J. Control Optim. 59, No. 1, 131-155 (2021). Reviewer: Kaïs Ammari (Monastir) MSC: 35Q74 74D05 93B05 93B07 93C20 PDF BibTeX XML Cite \textit{P. Guzman} and \textit{L. Rosier}, SIAM J. Control Optim. 59, No. 1, 131--155 (2021; Zbl 07299441) Full Text: DOI
Iokibe, Gaku Remark on a paper by Izadi and Baghalaghdam about cubes and fifth powers sums. (English) Zbl 07287133 Math. J. Okayama Univ. 63, 53-60 (2021). MSC: 11D41 11D45 14H52 PDF BibTeX XML Cite \textit{G. Iokibe}, Math. J. Okayama Univ. 63, 53--60 (2021; Zbl 07287133) Full Text: Link
Sharipov, R. A. Symmetry-based approach to the problem of a perfect cuboid. (English. Russian original) Zbl 07283018 J. Math. Sci., New York 252, No. 2, 266-282 (2021); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 152, 143-158 (2018). MSC: 11D09 11D41 11D72 PDF BibTeX XML Cite \textit{R. A. Sharipov}, J. Math. Sci., New York 252, No. 2, 266--282 (2021; Zbl 07283018); translation from Itogi Nauki Tekh., Ser. Sovrem. Mat. Prilozh., Temat. Obz. 152, 143--158 (2018) Full Text: DOI
Kebli, Salima; Kihel, Omar; Larone, Jesse; Luca, Florian On the nonnegative integer solutions to the equation \(F_n \pm F_m = y^a\). (English) Zbl 07276978 J. Number Theory 220, 107-127 (2021). MSC: 11B39 11J86 11D61 PDF BibTeX XML Cite \textit{S. Kebli} et al., J. Number Theory 220, 107--127 (2021; Zbl 07276978) Full Text: DOI
Dokchan, Rakporn; Pakapongpun, Apisit On the Diophantine equation \(p^x+(p+20)^y= z^2\), where \(p\) and \(p+20\) are primes. (English) Zbl 07264178 Int. J. Math. Comput. Sci. 16, No. 1, 179-183 (2021). MSC: 11D61 PDF BibTeX XML Cite \textit{R. Dokchan} and \textit{A. Pakapongpun}, Int. J. Math. Comput. Sci. 16, No. 1, 179--183 (2021; Zbl 07264178) Full Text: Link
Shabani-Solt, H.; Yusefnejad, N.; Janfada, A. S. On the Diophantine equation \(x^6+ky^3=z^6+kw^3\). (English) Zbl 07317621 Iran. J. Math. Sci. Inform. 15, No. 1, 15-21 (2020). MSC: 11G05 11G05 11D41 PDF BibTeX XML Cite \textit{H. Shabani-Solt} et al., Iran. J. Math. Sci. Inform. 15, No. 1, 15--21 (2020; Zbl 07317621) Full Text: Link
Mesnager, Sihem; Kim, Kwang Ho; Choe, Jong Hyok; Lee, Dok Nam Solving some affine equations over finite fields. (English) Zbl 07312728 Finite Fields Appl. 68, Article ID 101746, 20 p. (2020). MSC: 11D04 12E05 12E12 PDF BibTeX XML Cite \textit{S. Mesnager} et al., Finite Fields Appl. 68, Article ID 101746, 20 p. (2020; Zbl 07312728) Full Text: DOI
Park, Jinseo The extendibility of Diophantine pairs with property \(D(-1)\). (English) Zbl 07312265 Korean J. Math. 28, No. 3, 539-554 (2020). MSC: 11B39 11D09 11D45 PDF BibTeX XML Cite \textit{J. Park}, Korean J. Math. 28, No. 3, 539--554 (2020; Zbl 07312265) Full Text: DOI
Ladzoryshyn, N. B.; Petrychkovych, V. M.; Zelisko, H. V. Matrix Diophantine equations over quadratic rings and their solutions. (English) Zbl 07311922 Carpathian Math. Publ. 12, No. 2, 368-375 (2020). MSC: 15A24 11D09 PDF BibTeX XML Cite \textit{N. B. Ladzoryshyn} et al., Carpathian Math. Publ. 12, No. 2, 368--375 (2020; Zbl 07311922) Full Text: DOI
Galyautdinov, I. G.; Lavrentyeva, E. E. Diophantine equation generated by the maximal subfield of a circular field. (English. Russian original) Zbl 07309106 Russ. Math. 64, No. 7, 38-47 (2020); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45-55 (2020). MSC: 11R 11A 11D 11 11S PDF BibTeX XML Cite \textit{I. G. Galyautdinov} and \textit{E. E. Lavrentyeva}, Russ. Math. 64, No. 7, 38--47 (2020; Zbl 07309106); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2020, No. 7, 45--55 (2020) Full Text: DOI
Tchammou, E.; Togbé, A. On the Diophantine equation \(\sum_{j=1}^kjP_j^p=P_n^q\). (English) Zbl 07301206 Acta Math. Hung. 162, No. 2, 647-676 (2020). MSC: 11B39 11D45 PDF BibTeX XML Cite \textit{E. Tchammou} and \textit{A. Togbé}, Acta Math. Hung. 162, No. 2, 647--676 (2020; Zbl 07301206) Full Text: DOI
Fujita, Y.; Terai, N. On the generalized Ramanujan-Nagell equation \(x^2+(2c-1)^m=c^n\). (English) Zbl 07301197 Acta Math. Hung. 162, No. 2, 518-526 (2020). MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{Y. Fujita} and \textit{N. Terai}, Acta Math. Hung. 162, No. 2, 518--526 (2020; Zbl 07301197) Full Text: DOI
Earp-Lynch, B.; Earp-Lynch, S.; Kihel, O. On certain \(D(9)\) and \(D(64)\) Diophantine triples. (English) Zbl 07301196 Acta Math. Hung. 162, No. 2, 483-517 (2020). MSC: 11D09 11D45 11B37 11J86 PDF BibTeX XML Cite \textit{B. Earp-Lynch} et al., Acta Math. Hung. 162, No. 2, 483--517 (2020; Zbl 07301196) Full Text: DOI
Fu, Ruiqin; Yang, Hai A note on the exceptional solutions of Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 07301189 Period. Math. Hung. 81, No. 2, 275-283 (2020). MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{R. Fu} and \textit{H. Yang}, Period. Math. Hung. 81, No. 2, 275--283 (2020; Zbl 07301189) Full Text: DOI
Zhang, Yong; Shen, Zhongyan Arithmetic properties of polynomials. (English) Zbl 07301160 Period. Math. Hung. 81, No. 1, 134-148 (2020). MSC: 11D25 11D72 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{Z. Shen}, Period. Math. Hung. 81, No. 1, 134--148 (2020; Zbl 07301160) Full Text: DOI
Hirakawa, Yoshinosuke Counterexamples to the local-global principle associated with Swinnerton-Dyer’s cubic form. (English) Zbl 07297915 Rocky Mt. J. Math. 50, No. 6, 2097-2102 (2020). MSC: 11D57 11D41 11D72 11R18 PDF BibTeX XML Cite \textit{Y. Hirakawa}, Rocky Mt. J. Math. 50, No. 6, 2097--2102 (2020; Zbl 07297915) Full Text: DOI Euclid
Qu, Yunyun; Zeng, Jiwen On the solutions of the simultaneous Diophantine equations \({x^2} - 14{y^2} = 1\) and \({y^2} - d{z^2} = 16\). (Chinese. English summary) Zbl 07295912 J. Xiamen Univ., Nat. Sci. 59, No. 4, 512-515 (2020). MSC: 11D09 PDF BibTeX XML Cite \textit{Y. Qu} and \textit{J. Zeng}, J. Xiamen Univ., Nat. Sci. 59, No. 4, 512--515 (2020; Zbl 07295912) Full Text: DOI
Zhou, Xingwang A number theoretic method for high order correlation functions of the Ulam map. (English) Zbl 07295697 J. Sichuan Univ., Nat. Sci. Ed. 57, No. 3, 435-442 (2020). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{X. Zhou}, J. Sichuan Univ., Nat. Sci. Ed. 57, No. 3, 435--442 (2020; Zbl 07295697) Full Text: DOI
Li, Yuan; Luo, Jiagui Extension of the Stormer theorem. (Chinese. English summary) Zbl 07295530 J. Nat. Sci. Heilongjiang Univ. 37, No. 2, 167-172 (2020). MSC: 11D09 PDF BibTeX XML Cite \textit{Y. Li} and \textit{J. Luo}, J. Nat. Sci. Heilongjiang Univ. 37, No. 2, 167--172 (2020; Zbl 07295530) Full Text: DOI
Guan, Xungui On the common solutions of Pell equations \({x^2} - ({c^2} - 1){y^2} = {y^2} - 2{p_1}{p_2}{p_3}{z^2} = 1\). (Chinese. English summary) Zbl 07294918 Acta Math. Sin., Chin. Ser. 63, No. 2, 157-170 (2020). MSC: 11D09 PDF BibTeX XML Cite \textit{X. Guan}, Acta Math. Sin., Chin. Ser. 63, No. 2, 157--170 (2020; Zbl 07294918)
Andruszkiewicz, R. R.; Andruszkiewicz, N. Elementary proof of Nagell’s theorem. (English) Zbl 07293032 Azerb. J. Math. 10, No. 2, 62-70 (2020). MSC: 11D41 PDF BibTeX XML Cite \textit{R. R. Andruszkiewicz} and \textit{N. Andruszkiewicz}, Azerb. J. Math. 10, No. 2, 62--70 (2020; Zbl 07293032) Full Text: Link
Luca, F.; Szalay, L. On the equation \((2^k-1)(3^l-1)=5^m-1\). (English) Zbl 07293028 Azerb. J. Math. 10, No. 2, 3-11 (2020). MSC: 11A25 11B39 11J86 PDF BibTeX XML Cite \textit{F. Luca} and \textit{L. Szalay}, Azerb. J. Math. 10, No. 2, 3--11 (2020; Zbl 07293028) Full Text: Link
Zhang, Shaohua; Shi, Wujie On the number of simple \(K_4\) groups. (English) Zbl 07290386 Bull. Iran. Math. Soc. 46, No. 6, 1669-1674 (2020). MSC: 11D61 11D45 20D05 PDF BibTeX XML Cite \textit{S. Zhang} and \textit{W. Shi}, Bull. Iran. Math. Soc. 46, No. 6, 1669--1674 (2020; Zbl 07290386) Full Text: DOI
Kizildere, Elif; Le, Maohua; Soydan, Gökhan A note on the ternary purely exponential Diophantine equation \(A^x+B^y=C^z\) with \(A+B=C^2\). (English) Zbl 07287397 Stud. Sci. Math. Hung. 57, No. 2, 200-206 (2020). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D61 11B39 PDF BibTeX XML Cite \textit{E. Kizildere} et al., Stud. Sci. Math. Hung. 57, No. 2, 200--206 (2020; Zbl 07287397) Full Text: DOI
Hashem, H. H. G.; El-Sayed, A. M. A. Existence results for a quadratic integral equation of fractional order by a certain function. (English) Zbl 07282706 Fixed Point Theory 21, No. 1, 181-190 (2020). MSC: 45 11D09 47H10 PDF BibTeX XML Cite \textit{H. H. G. Hashem} and \textit{A. M. A. El-Sayed}, Fixed Point Theory 21, No. 1, 181--190 (2020; Zbl 07282706) Full Text: Link
Bugeaud, Yann Effective simultaneous rational approximation to pairs of real quadratic numbers. (English) Zbl 07272354 Mosc. J. Comb. Number Theory 9, No. 4, 353-360 (2020). Reviewer: István Gaál (Debrecen) MSC: 11J13 11D09 11J86 PDF BibTeX XML Cite \textit{Y. Bugeaud}, Mosc. J. Comb. Number Theory 9, No. 4, 353--360 (2020; Zbl 07272354) Full Text: DOI
Ddamulira, Mahadi; Luca, Florian The \(x\)-coordinates of Pell equations and sums of two Fibonacci numbers. II. (English) Zbl 07271355 Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 58, 20 p. (2020). MSC: 11B39 11D45 11D61 11J86 PDF BibTeX XML Cite \textit{M. Ddamulira} and \textit{F. Luca}, Proc. Indian Acad. Sci., Math. Sci. 130, No. 1, Paper No. 58, 20 p. (2020; Zbl 07271355) Full Text: DOI
Li, Changji The solvability of equation \({\varphi_2} ({\varphi_3} (n)) = 3^{\omega (n)}\). (Chinese. English summary) Zbl 07267453 Math. Pract. Theory 50, No. 8, 302-306 (2020). MSC: 11B68 11B83 PDF BibTeX XML Cite \textit{C. Li}, Math. Pract. Theory 50, No. 8, 302--306 (2020; Zbl 07267453)
Zheng, Hui; Yang, Shichun The solutions of the equation of preimage distribution for a class of perfect nonlinear functions. (Chinese. English summary) Zbl 07267379 Math. Pract. Theory 50, No. 4, 263-268 (2020). MSC: 20F70 PDF BibTeX XML Cite \textit{H. Zheng} and \textit{S. Yang}, Math. Pract. Theory 50, No. 4, 263--268 (2020; Zbl 07267379)
Guan, Xungui On the Diophantine equation \(x^2-2y^4=M (M=17, 41, 73, 89, 97)\). (Chinese. English summary) Zbl 07266675 J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200-206 (2020). MSC: 11D25 PDF BibTeX XML Cite \textit{X. Guan}, J. Cent. China Norm. Univ., Nat. Sci. 54, No. 2, 200--206 (2020; Zbl 07266675) Full Text: DOI
Zhang, Mingli; Gao, Li On the positive integer solution of a ternary variable coefficient Euler function equation. (Chinese. English summary) Zbl 07266664 J. Cent. China Norm. Univ., Nat. Sci. 54, No. 1, 23-29 (2020). MSC: 11B68 11D72 PDF BibTeX XML Cite \textit{M. Zhang} and \textit{L. Gao}, J. Cent. China Norm. Univ., Nat. Sci. 54, No. 1, 23--29 (2020; Zbl 07266664) Full Text: DOI
Dou, Xiaoxia A class of Diophantine equation. (Chinese. English summary) Zbl 07266361 Acta Sci. Nat. Univ. Sunyatseni 59, No. 2, 15-21 (2020). MSC: 11D09 PDF BibTeX XML Cite \textit{X. Dou}, Acta Sci. Nat. Univ. Sunyatseni 59, No. 2, 15--21 (2020; Zbl 07266361) Full Text: DOI
Bai, Hairong; Kızıldere, Elif; Soydan, Gökhan; Yuan, Pingzhi On the exponential Diophantine equation \((n-1)^x+(n+2)^y=n^z\). (English) Zbl 07262535 Colloq. Math. 161, No. 2, 239-249 (2020). MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{H. Bai} et al., Colloq. Math. 161, No. 2, 239--249 (2020; Zbl 07262535) Full Text: DOI
Edjeou, Bilizimbéyé; Tall, Amadou; Ben Maaouia, Mohamed Ben Fraj Powers of two as sums of three Lucas numbers. (English) Zbl 07261888 J. Integer Seq. 23, No. 8, Article 20.8.8, 16 p. (2020). MSC: 11B39 11J86 PDF BibTeX XML Cite \textit{B. Edjeou} et al., J. Integer Seq. 23, No. 8, Article 20.8.8, 16 p. (2020; Zbl 07261888) Full Text: Link
Liptai, Kálmán; Németh, László; Soydan, Gökhan; Szalay, László Resolution of the equation \((3^{x_{1}}-1)(3^{x_{2}}-1)=(5^{y_{1}}-1)(5^{y_{2}}-1)\). (English) Zbl 07261872 Rocky Mt. J. Math. 50, No. 4, 1425-1433 (2020). MSC: 11D61 11B37 33-XX PDF BibTeX XML Cite \textit{K. Liptai} et al., Rocky Mt. J. Math. 50, No. 4, 1425--1433 (2020; Zbl 07261872) Full Text: DOI Euclid
Işik, Erman; Kara, Yasemin; Özman, Ekin On ternary Diophantine equations of signature \((p,p,2)\) over number fields. (English) Zbl 07259216 Turk. J. Math. 44, No. 4, 1197-1211 (2020). MSC: 11D41 11G05 11D45 PDF BibTeX XML Cite \textit{E. Işik} et al., Turk. J. Math. 44, No. 4, 1197--1211 (2020; Zbl 07259216) Full Text: DOI
Hajdu, L.; Papp, Á. Polynomial values of products of terms from an arithmetic progression. (English) Zbl 1453.11048 Monatsh. Math. 193, No. 3, 637-655 (2020). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11D41 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{Á. Papp}, Monatsh. Math. 193, No. 3, 637--655 (2020; Zbl 1453.11048) Full Text: DOI
Yan, Xiao-Hui The Diophantine equation \((m^2+n^2)^x+(2mn)^y=(m+n)^{2z}\). (English) Zbl 07257246 Int. J. Number Theory 16, No. 8, 1701-1708 (2020). MSC: 11D61 PDF BibTeX XML Cite \textit{X.-H. Yan}, Int. J. Number Theory 16, No. 8, 1701--1708 (2020; Zbl 07257246) Full Text: DOI
Kizildere, Elif; Soydan, Gokhan On the Diophantine equation \((5pn^2 - 1)^x + (p(p - 5)n^2 + 1)^y=(pn)^z\). (English) Zbl 07254059 Honam Math. J. 42, No. 1, 139-150 (2020). MSC: 11D61 PDF BibTeX XML Cite \textit{E. Kizildere} and \textit{G. Soydan}, Honam Math. J. 42, No. 1, 139--150 (2020; Zbl 07254059) Full Text: DOI
Nathanson, Melvyn B. Geometric progressions in syndetic sets. (English) Zbl 07245795 Arch. Math. 115, No. 4, 413-417 (2020). MSC: 11B05 11B75 11D09 11R11 PDF BibTeX XML Cite \textit{M. B. Nathanson}, Arch. Math. 115, No. 4, 413--417 (2020; Zbl 07245795) Full Text: DOI
Sahukar, M. K.; Panda, G. K. Balancing and balancing-like numbers which are one away from perfect powers. (English) Zbl 07245589 Bull. Braz. Math. Soc. (N.S.) 51, No. 3, 681-696 (2020). MSC: 11B39 PDF BibTeX XML Cite \textit{M. K. Sahukar} and \textit{G. K. Panda}, Bull. Braz. Math. Soc. (N.S.) 51, No. 3, 681--696 (2020; Zbl 07245589) Full Text: DOI
Gugushvili, Shota; Mariucci, Ester; van der Meulen, Frank Decompounding discrete distributions: a nonparametric Bayesian approach. (English) Zbl 1450.62029 Scand. J. Stat. 47, No. 2, 464-492 (2020). MSC: 62G07 60G55 PDF BibTeX XML Cite \textit{S. Gugushvili} et al., Scand. J. Stat. 47, No. 2, 464--492 (2020; Zbl 1450.62029) Full Text: DOI
Dan-Cohen, Ishai Mixed Tate motives and the unit equation. II. (English) Zbl 1452.11076 Algebra Number Theory 14, No. 5, 1175-1237 (2020). Reviewer: Fangzhou Jin (Essen) MSC: 11G55 11D45 14F30 14F35 14F42 14G05 PDF BibTeX XML Cite \textit{I. Dan-Cohen}, Algebra Number Theory 14, No. 5, 1175--1237 (2020; Zbl 1452.11076) Full Text: DOI
Noubissie, Armand; Togbé, Alain; Zhang, Zhongfeng On the exponential Diophantine equation \((a^n-1)(b^n-1)=x^2\). (English) Zbl 07242764 Bull. Belg. Math. Soc. - Simon Stevin 27, No. 2, 161-166 (2020). MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{A. Noubissie} et al., Bull. Belg. Math. Soc. - Simon Stevin 27, No. 2, 161--166 (2020; Zbl 07242764) Full Text: DOI Euclid
Tengely, Szabolcs; Ulas, Maciej; Zygadło, Jakub On a Diophantine equation of Erdős and Graham. (English) Zbl 07242319 J. Number Theory 217, 445-459 (2020). Reviewer: István Gaál (Debrecen) MSC: 11D68 11A63 PDF BibTeX XML Cite \textit{S. Tengely} et al., J. Number Theory 217, 445--459 (2020; Zbl 07242319) Full Text: DOI
Hajdu, L.; Sebestyén, P. Sums of \(S\)-units in the solution sets of generalized Pell equations. (English) Zbl 07238497 Arch. Math. 115, No. 3, 279-287 (2020). MSC: 11D09 11D61 11B37 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{P. Sebestyén}, Arch. Math. 115, No. 3, 279--287 (2020; Zbl 07238497) Full Text: DOI
Balfaqih, Abdulrahman; Kamarulhaili, Hailiza New result on Jeśmanowicz’ conjecture. (English) Zbl 07235554 Int. J. Math. Comput. Sci. 15, No. 3, 963-973 (2020). MSC: 11D61 11A07 PDF BibTeX XML Cite \textit{A. Balfaqih} and \textit{H. Kamarulhaili}, Int. J. Math. Comput. Sci. 15, No. 3, 963--973 (2020; Zbl 07235554) Full Text: Link
Dąbrowski, Andrzej; Günhan, Nursena; Soydan, Gökhan On a class of Lebesgue-Ljunggren-Nagell type equations. (English) Zbl 07226721 J. Number Theory 215, 149-159 (2020). MSC: 11D61 11B39 PDF BibTeX XML Cite \textit{A. Dąbrowski} et al., J. Number Theory 215, 149--159 (2020; Zbl 07226721) Full Text: DOI
Zhang, Yong; Zargar, Arman Shamsi On the Diophantine equations \(z^2=f(x)^2 \pm f(y)^2\) involving Laurent polynomials. (English) Zbl 1450.11029 Funct. Approximatio, Comment. Math. 62, No. 2, 187-201 (2020). Reviewer: Maciej Ulas (Kraków) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{A. S. Zargar}, Funct. Approximatio, Comment. Math. 62, No. 2, 187--201 (2020; Zbl 1450.11029) Full Text: DOI Euclid
Das, Pranabesh; Dey, Pallab Kanti; Maji, Bibekananda; Rout, Sudhansu Sekhar Perfect powers in an alternating sum of consecutive cubes. (English) Zbl 07222699 Glas. Mat., III. Ser. 55, No. 1, 37-53 (2020). MSC: 11D61 11D41 11F11 11F80 PDF BibTeX XML Cite \textit{P. Das} et al., Glas. Mat., III. Ser. 55, No. 1, 37--53 (2020; Zbl 07222699) Full Text: DOI
Tengelys, Szabolcs Markoff-Rosenberger triples with Fibonacci components. (English) Zbl 07222698 Glas. Mat., III. Ser. 55, No. 1, 29-36 (2020). Reviewer: Anitha Srinivasan (Madrid) MSC: 11D45 11D25 11B39 PDF BibTeX XML Cite \textit{S. Tengelys}, Glas. Mat., III. Ser. 55, No. 1, 29--36 (2020; Zbl 07222698) Full Text: DOI
Bazsó, András; Bérczes, Attila; Kolouch, Ondřej; Pink, István; Šustek, Jan Diophantine equations connected to the Komornik polynomials. (English) Zbl 07222697 Glas. Mat., III. Ser. 55, No. 1, 13-27 (2020). MSC: 11D41 11B83 11D41 11B68 11B65 11J86 PDF BibTeX XML Cite \textit{A. Bazsó} et al., Glas. Mat., III. Ser. 55, No. 1, 13--27 (2020; Zbl 07222697) Full Text: DOI
Bennett, Michael A.; Gherga, Adela; Kreso, Dijana An old and new approach to Goormaghtigh’s equation. (English) Zbl 07222182 Trans. Am. Math. Soc. 373, No. 8, 5707-5745 (2020). MSC: 11D41 11D61 11J68 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Trans. Am. Math. Soc. 373, No. 8, 5707--5745 (2020; Zbl 07222182) Full Text: DOI
Badr, Eslam; Bars, Francesc Hypersurface model-fields of definition for smooth hypersurfaces and their twists. (English) Zbl 1442.14137 Acta Arith. 194, No. 3, 267-280 (2020). MSC: 14J70 11D72 11D41 14J50 14F22 PDF BibTeX XML Cite \textit{E. Badr} and \textit{F. Bars}, Acta Arith. 194, No. 3, 267--280 (2020; Zbl 1442.14137) Full Text: DOI
Alvanos, Paraskevas; Poulakis, Dimitrios Bounds for the smallest integral point on a conic over a number field. (English) Zbl 1450.11021 Acta Arith. 193, No. 4, 355-368 (2020). Reviewer: Mahadi Ddamulira (Saarbrücken) MSC: 11D09 14G25 14H25 PDF BibTeX XML Cite \textit{P. Alvanos} and \textit{D. Poulakis}, Acta Arith. 193, No. 4, 355--368 (2020; Zbl 1450.11021) Full Text: DOI
Takeda, Wataru Explicit upper bound of the solution-free region for a Diophantine equation over number fields. (English) Zbl 07220257 Lith. Math. J. 60, No. 1, 107-128 (2020). MSC: 11D45 11D57 11D72 PDF BibTeX XML Cite \textit{W. Takeda}, Lith. Math. J. 60, No. 1, 107--128 (2020; Zbl 07220257) Full Text: DOI
Sharma, Richa On Lebesgue-Ramanujan-Nagell type equations. (English) Zbl 1447.11053 Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer. 147-161 (2020). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{R. Sharma}, in: Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4--7, 2017. Singapore: Springer. 147--161 (2020; Zbl 1447.11053) Full Text: DOI
Waldschmidt, Michel Thue Diophantine equations. (English) Zbl 07220059 Chakraborty, Kalyan (ed.) et al., Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4–7, 2017. Singapore: Springer (ISBN 978-981-15-1513-2/hbk; 978-981-15-1516-3/pbk; 978-981-15-1514-9/ebook). 25-41 (2020). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D59 11J68 11J86 PDF BibTeX XML Cite \textit{M. Waldschmidt}, in: Class groups of number fields and related topics. Collected papers presented at the first international conference, ICCGNFRT, Harish-Chandra Research Institute, Allahabad, India, September 4--7, 2017. Singapore: Springer. 25--41 (2020; Zbl 07220059) Full Text: DOI
Chilikov, A. A.; Efremov, I.; Zveryk, V.; Khomich, N. A combinatorial proof of simplified Kollár’s theorem on Pell’s equations. (English. Russian original) Zbl 07215598 Math. Notes 107, No. 5, 867-871 (2020); translation from Mat. Zametki 107, No. 5, 796-800 (2020). Reviewer: Alexei Kanel-Belov (Ramat-Gan) MSC: 14J26 14G25 11D09 14R25 11D57 PDF BibTeX XML Cite \textit{A. A. Chilikov} et al., Math. Notes 107, No. 5, 867--871 (2020; Zbl 07215598); translation from Mat. Zametki 107, No. 5, 796--800 (2020) Full Text: DOI
Skresanov, S. V. Group topologies on the integers and \(S\)-unit equations. (English. Russian original) Zbl 1440.22001 Sib. Math. J. 61, No. 3, 542-544 (2020); translation from Sib. Mat. Zh. 61, No. 3, 687-691 (2020). Reviewer: Nikolay I. Kryuchkov (Ryazan) MSC: 22A05 11B05 PDF BibTeX XML Cite \textit{S. V. Skresanov}, Sib. Math. J. 61, No. 3, 542--544 (2020; Zbl 1440.22001); translation from Sib. Mat. Zh. 61, No. 3, 687--691 (2020) Full Text: DOI
Binner, Damanvir Singh The number of solutions to \(ax + by + cz = n\) and its relation to quadratic residues. (English) Zbl 07212811 J. Integer Seq. 23, No. 6, Article 20.6.5, 19 p. (2020). MSC: 11D45 05A15 11A15 11A05 11A07 11D04 11D72 PDF BibTeX XML Cite \textit{D. S. Binner}, J. Integer Seq. 23, No. 6, Article 20.6.5, 19 p. (2020; Zbl 07212811) Full Text: Link
Argáez-García, Alejandro; Patel, Vandita On perfect powers that are sums of cubes of a seven term arithmetic progression. (English) Zbl 07207003 J. Number Theory 214, 440-451 (2020). MSC: 11D61 11D41 11D59 11J86 PDF BibTeX XML Cite \textit{A. Argáez-García} and \textit{V. Patel}, J. Number Theory 214, 440--451 (2020; Zbl 07207003) Full Text: DOI
Kara, Yasemin; Ozman, Ekin Asymptotic generalized Fermat’s last theorem over number fields. (English) Zbl 07205408 Int. J. Number Theory 16, No. 5, 907-924 (2020). MSC: 11Dxx 11Gxx 14Gxx PDF BibTeX XML Cite \textit{Y. Kara} and \textit{E. Ozman}, Int. J. Number Theory 16, No. 5, 907--924 (2020; Zbl 07205408) Full Text: DOI
Karaliolios, Nikolaos Fibered rotation vector and hypoellipticity for quasi-periodic cocycles in compact Lie groups. (English) Zbl 1448.35108 Bull. Lond. Math. Soc. 52, No. 1, 224-236 (2020). MSC: 35H10 37C55 PDF BibTeX XML Cite \textit{N. Karaliolios}, Bull. Lond. Math. Soc. 52, No. 1, 224--236 (2020; Zbl 1448.35108) Full Text: DOI
Kollár, János Pell surfaces. (English) Zbl 07200111 Acta Math. Hung. 160, No. 2, 478-518 (2020). MSC: 14J26 14G25 11D09 14R25 11D57 PDF BibTeX XML Cite \textit{J. Kollár}, Acta Math. Hung. 160, No. 2, 478--518 (2020; Zbl 07200111) Full Text: DOI
Kushwaha, Seema Pell equation: a revisit through periodic \(\mathcal{F}_{2^l}\)-continued fractions. (English) Zbl 1434.11021 Integers 20A, Paper A9, 13 p. (2020). MSC: 11A55 11D09 PDF BibTeX XML Cite \textit{S. Kushwaha}, Integers 20A, Paper A9, 13 p. (2020; Zbl 1434.11021) Full Text: Link
Koutsianas, Angelos On the generalized Fermat equation \(a^2+3b^6=c^n\). (English) Zbl 07198877 Bull. Hell. Math. Soc. 64, 56-68 (2020). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11D61 PDF BibTeX XML Cite \textit{A. Koutsianas}, Bull. Hell. Math. Soc. 64, 56--68 (2020; Zbl 07198877) Full Text: Link
Elsholtz, Christian; Planitzer, Stefan The number of solutions of the Erdős-Straus equation and sums of \(k\) unit fractions. (English) Zbl 07193438 Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 3, 1401-1427 (2020). MSC: 11D68 11D72 PDF BibTeX XML Cite \textit{C. Elsholtz} and \textit{S. Planitzer}, Proc. R. Soc. Edinb., Sect. A, Math. 150, No. 3, 1401--1427 (2020; Zbl 07193438) Full Text: DOI
Gueth, Krisztián; Luca, Florian; Szalay, László On a Diophantine equation involving powers of Fibonacci numbers. (English) Zbl 07192786 Proc. Japan Acad., Ser. A 96, No. 4, 33-37 (2020). MSC: 11B39 11D45 PDF BibTeX XML Cite \textit{K. Gueth} et al., Proc. Japan Acad., Ser. A 96, No. 4, 33--37 (2020; Zbl 07192786) Full Text: DOI Euclid
Krug, Konrad The hitchhickers guide to the integers: the case 42. (The hitchhickers guide to the integers: die Sache mit der 42.) (German) Zbl 07192307 Mitt. Dtsch. Math.-Ver. 27, No. 3-4, 124-125 (2020). MSC: 11D25 11D41 PDF BibTeX XML Cite \textit{K. Krug}, Mitt. Dtsch. Math.-Ver. 27, No. 3--4, 124--125 (2020; Zbl 07192307) Full Text: DOI
Harris, Zachary; Louwsma, Joel On arithmetical structures on complete graphs. (English) Zbl 07184488 Involve 13, No. 2, 345-355 (2020). MSC: 11D68 05C50 11A41 PDF BibTeX XML Cite \textit{Z. Harris} and \textit{J. Louwsma}, Involve 13, No. 2, 345--355 (2020; Zbl 07184488) Full Text: DOI
Gómez, Carlos A.; Luca, Florian Zeckendorf representations with at most two terms to \(x\)-coordinates of Pell equations. (English) Zbl 07184420 Sci. China, Math. 63, No. 4, 627-642 (2020). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11D61 11J86 PDF BibTeX XML Cite \textit{C. A. Gómez} and \textit{F. Luca}, Sci. China, Math. 63, No. 4, 627--642 (2020; Zbl 07184420) Full Text: DOI
Luo, Wenyu; Yuan, Pingzhi On the Diophantine equation \(\frac{ax^{n+2l}+c}{abt^2x^n+d}=by^2\). (English) Zbl 1432.11037 Integers 20, Paper A15, 13 p. (2020). MSC: 11D61 11D09 PDF BibTeX XML Cite \textit{W. Luo} and \textit{P. Yuan}, Integers 20, Paper A15, 13 p. (2020; Zbl 1432.11037) Full Text: Link
Adegbindin, Chèfiath; Luca, Florian; Togbé, Alain Pell and Pell-Lucas numbers as sums of two repdigits. (English) Zbl 1452.11020 Bull. Malays. Math. Sci. Soc. (2) 43, No. 2, 1253-1271 (2020). MSC: 11B39 11D09 11J86 PDF BibTeX XML Cite \textit{C. Adegbindin} et al., Bull. Malays. Math. Sci. Soc. (2) 43, No. 2, 1253--1271 (2020; Zbl 1452.11020) Full Text: DOI
Faye, Bernadette; Luca, Florian On \(Y\)-coordinates of Pell equations which are members of a fixed binary recurrence. (English) Zbl 07179055 New York J. Math. 26, 184-206 (2020). MSC: 11D61 11B39 11D45 PDF BibTeX XML Cite \textit{B. Faye} and \textit{F. Luca}, New York J. Math. 26, 184--206 (2020; Zbl 07179055) Full Text: Link
Koymans, Peter; Pagano, Carlo Unit equations and Fermat surfaces in positive characteristic. (English) Zbl 07178802 Acta Arith. 193, No. 2, 133-156 (2020). Reviewer: István Gaál (Debrecen) MSC: 11D41 11D61 PDF BibTeX XML Cite \textit{P. Koymans} and \textit{C. Pagano}, Acta Arith. 193, No. 2, 133--156 (2020; Zbl 07178802) Full Text: DOI
Bennett, Michael A.; Garbuz, Ben; Marten, Adam Goormaghtigh’s equation: small parameters. (English) Zbl 1449.11059 Publ. Math. 96, No. 1-2, 91-110 (2020). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11D61 11J68 11Y50 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Publ. Math. 96, No. 1--2, 91--110 (2020; Zbl 1449.11059) Full Text: DOI
Bravo, Eric F.; Gómez Ruiz, Carlos Alexis; Luca, Florian Correction to: \(X\)-coordinates of Pell equations as sums of two tribonacci numbers. (English) Zbl 1449.11051 Period. Math. Hung. 46, No. 1, 145-146 (2020). MSC: 11D09 11B39 11J86 PDF BibTeX XML Cite \textit{E. F. Bravo} et al., Period. Math. Hung. 46, No. 1, 145--146 (2020; Zbl 1449.11051) Full Text: DOI
Zhang, Yong; Chen, Deyi A Diophantine equation with the harmonic mean. (English) Zbl 1449.11070 Period. Math. Hung. 46, No. 1, 138-144 (2020). Reviewer: Thomas A. Schmidt (Corvallis) MSC: 11D72 11D25 11D41 11G05 PDF BibTeX XML Cite \textit{Y. Zhang} and \textit{D. Chen}, Period. Math. Hung. 46, No. 1, 138--144 (2020; Zbl 1449.11070) Full Text: DOI
Le, Maohua; Soydan, Gökhan An application of Baker’s method to the Jeśmanowicz’ conjecture on primitive Pythagorean triples. (English) Zbl 1449.11066 Period. Math. Hung. 46, No. 1, 74-80 (2020). Reviewer: Artūras Dubickas (Vilnius) MSC: 11D61 11J86 PDF BibTeX XML Cite \textit{M. Le} and \textit{G. Soydan}, Period. Math. Hung. 46, No. 1, 74--80 (2020; Zbl 1449.11066) Full Text: DOI
Ha, J.; Soundararajan, K. Many solutions to the \(S\)-unit equation \(a+1=c\). (English) Zbl 1449.11061 Acta Math. Hung. 160, No. 1, 153-160 (2020). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D45 11D72 11P55 PDF BibTeX XML Cite \textit{J. Ha} and \textit{K. Soundararajan}, Acta Math. Hung. 160, No. 1, 153--160 (2020; Zbl 1449.11061) Full Text: DOI
Sawa, Masanori; Uchida, Yukihiro Algebro-geometric aspects of the Christoffel-Darboux kernels for classical orthogonal polynomials. (English) Zbl 1433.42032 Trans. Am. Math. Soc. 373, No. 2, 1243-1264 (2020). MSC: 42C05 33C45 65D32 11D72 PDF BibTeX XML Cite \textit{M. Sawa} and \textit{Y. Uchida}, Trans. Am. Math. Soc. 373, No. 2, 1243--1264 (2020; Zbl 1433.42032) Full Text: DOI
Jiang, Kun; Gao, Wei; Cao, Wei Counting solutions to generalized Markoff-Hurwitz-type equations in finite fields. (English) Zbl 1452.11146 Finite Fields Appl. 62, Article ID 101609, 11 p. (2020). MSC: 11T06 11T24 11D45 PDF BibTeX XML Cite \textit{K. Jiang} et al., Finite Fields Appl. 62, Article ID 101609, 11 p. (2020; Zbl 1452.11146) Full Text: DOI
Bennett, Michael; Siksek, Samir A conjecture of Erdős, supersingular primes and short character sums. (English) Zbl 1440.11039 Ann. Math. (2) 191, No. 2, 355-392 (2020). Reviewer: Mahadi Ddamulira (Graz) MSC: 11D61 11D41 11F80 11F41 PDF BibTeX XML Cite \textit{M. Bennett} and \textit{S. Siksek}, Ann. Math. (2) 191, No. 2, 355--392 (2020; Zbl 1440.11039) Full Text: DOI
Bencherif, Farid; Boumahdi, Rachid; Garici, Tarek; Schedler, Zak Upper bounds for the number of solutions for the Diophantine equation \(y^2=px( Ax^2-C)(C=2,\pm 1,\pm 4) \). (English) Zbl 07167308 Colloq. Math. 159, No. 2, 243-257 (2020). MSC: 11D25 11B39 PDF BibTeX XML Cite \textit{F. Bencherif} et al., Colloq. Math. 159, No. 2, 243--257 (2020; Zbl 07167308) Full Text: DOI
Freitas, Nuno; Kraus, Alain; Siksek, Samir Class field theory, Diophantine analysis and the asymptotic Fermat’s last theorem. (English) Zbl 1450.11023 Adv. Math. 363, Article ID 106964, 37 p. (2020). Reviewer: Mahadi Ddamulira (Saarbrücken) MSC: 11D41 11R37 11J86 PDF BibTeX XML Cite \textit{N. Freitas} et al., Adv. Math. 363, Article ID 106964, 37 p. (2020; Zbl 1450.11023) Full Text: DOI
Prempreesuk, Bencharat; Noppakaew, Passawan; Pongsriiam, Prapanpong Zeckendorf representation and multiplicative inverse of \(F_m\bmod F_n\). (English) Zbl 07159540 Int. J. Math. Comput. Sci. 15, No. 1, 17-25 (2020). MSC: 11B39 PDF BibTeX XML Cite \textit{B. Prempreesuk} et al., Int. J. Math. Comput. Sci. 15, No. 1, 17--25 (2020; Zbl 07159540) Full Text: Link
Hajdu, Lajos On special extrema of polynomials with applications to Diophantine problems. (English) Zbl 1450.11019 Res. Number Theory 6, No. 1, Paper No. 3, 14 p. (2020). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11C08 11D41 11B39 PDF BibTeX XML Cite \textit{L. Hajdu}, Res. Number Theory 6, No. 1, Paper No. 3, 14 p. (2020; Zbl 1450.11019) Full Text: DOI
Gallegos-Ruiz, H. R.; Katsipis, N.; Tengely, Sz.; Ulas, M. On the Diophantine equation \(\binom{n}{k} = \binom{m}{l} + d\). (English) Zbl 1451.11020 J. Number Theory 208, 418-440 (2020). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D25 11D41 11G30 11G05 11J86 PDF BibTeX XML Cite \textit{H. R. Gallegos-Ruiz} et al., J. Number Theory 208, 418--440 (2020; Zbl 1451.11020) Full Text: DOI
Ddamulira, Mahadi; Luca, Florian On the \(x\)-coordinates of Pell equations which are \(k\)-generalized Fibonacci numbers. (English) Zbl 1447.11025 J. Number Theory 207, 156-195 (2020). MSC: 11B39 11D09 11J86 PDF BibTeX XML Cite \textit{M. Ddamulira} and \textit{F. Luca}, J. Number Theory 207, 156--195 (2020; Zbl 1447.11025) Full Text: DOI arXiv
Pachev, Urusbi Mukhamedovich; Shakova, T. A. On units of a quaternion order of an indefinite anisotropic ternary quadratic form. (Russian. English summary) Zbl 07310015 Chebyshevskiĭ Sb. 20, No. 4(72), 270-280 (2019). MSC: 11E88 11R52 11D09 PDF BibTeX XML Cite \textit{U. M. Pachev} and \textit{T. A. Shakova}, Chebyshevskiĭ Sb. 20, No. 4(72), 270--280 (2019; Zbl 07310015) Full Text: DOI MNR
Keskin, Refik; Şiar, Zafer; Duman, Merve Güney Solutions of some Diophantine equations in terms of Horadam sequence. (English) Zbl 07300669 Trans. A. Razmadze Math. Inst. 173, No. 3, 79-91 (2019). MSC: 11D09 11B39 PDF BibTeX XML Cite \textit{R. Keskin} et al., Trans. A. Razmadze Math. Inst. 173, No. 3, 79--91 (2019; Zbl 07300669) Full Text: Link
Petrychkovych, V. M. Standard forms of matrices over rings with respect to different types of equivalences and their applications in theory of the matrix factorization and matrix equations. (Ukrainian, English) Zbl 07286254 Mat. Metody Fiz.-Mekh. Polya 62, No. 4, 7-27 (2019). Reviewer: Anatoly Martynyuk (Kyïv) MSC: 15A24 15A30 11D99 PDF BibTeX XML Cite \textit{V. M. Petrychkovych}, Mat. Metody Fiz.-Mekh. Polya 62, No. 4, 7--27 (2019; Zbl 07286254)
Ramasamy, A. M. S. Polynomials yielding quadruples with property D(k). (English) Zbl 07282734 J. Ramanujan Soc. Math. Math. Sci. 7, No. 1, 53-64 (2019). MSC: 11B37 11B83 11D09 PDF BibTeX XML Cite \textit{A. M. S. Ramasamy}, J. Ramanujan Soc. Math. Math. Sci. 7, No. 1, 53--64 (2019; Zbl 07282734) Full Text: Link
Hayat, Umar; Amanullah, Shahid; Walsh, Shane; Abdullah, Mamoon; Bustamante, Miguel D. Discrete resonant Rossby/drift wave triads: explicit parameterisations and a fast direct numerical search algorithm. (English) Zbl 07264524 Commun. Nonlinear Sci. Numer. Simul. 79, Article ID 104896, 19 p. (2019). MSC: 76U65 76M99 PDF BibTeX XML Cite \textit{U. Hayat} et al., Commun. Nonlinear Sci. Numer. Simul. 79, Article ID 104896, 19 p. (2019; Zbl 07264524) Full Text: DOI
Zheng, Tao; Xia, Bican An effective framework for constructing exponent lattice basis of nonzero algebraic numbers. (English) Zbl 07246269 Bradford, Russell (ed.), Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC ’19, Beijing, China, July 15–18, 2019. New York, NY: Association for Computing Machinery (ACM) (ISBN 978-1-4503-6084-5). 371-378 (2019). MSC: 68W30 PDF BibTeX XML Cite \textit{T. Zheng} and \textit{B. Xia}, in: Proceedings of the 44th international symposium on symbolic and algebraic computation, ISSAC '19, Beijing, China, July 15--18, 2019. New York, NY: Association for Computing Machinery (ACM). 371--378 (2019; Zbl 07246269) Full Text: DOI