Kumar, Narasimha; Sahoo, Satyabrat On the solutions of \(x^p+y^p=2^r z^p\), \(x^p+y^p=z^2\) over totally real fields. (English) Zbl 07810306 Acta Arith. 212, No. 1, 31-47 (2024). MSC: 11D41 11F80 11R04 11R80 PDFBibTeX XMLCite \textit{N. Kumar} and \textit{S. Sahoo}, Acta Arith. 212, No. 1, 31--47 (2024; Zbl 07810306) Full Text: DOI arXiv
Pasten, Hector Shimura curves and the abc conjecture. (English) Zbl 07748223 J. Number Theory 254, 214-335 (2024). MSC: 11G18 11G05 14G40 PDFBibTeX XMLCite \textit{H. Pasten}, J. Number Theory 254, 214--335 (2024; Zbl 07748223) Full Text: DOI arXiv
Fujita, Yasutsugu; Le, Maohua; Terai, Nobuhiro A note on the solution to the generalized Ramanujan-Nagell equation \(x^2+(4c)^y=(c+1)^z\). (English) Zbl 07778481 Indian J. Pure Appl. Math. 54, No. 4, 1145-1157 (2023). Reviewer: Ingrid Vukusic (Salzburg) MSC: 11D61 PDFBibTeX XMLCite \textit{Y. Fujita} et al., Indian J. Pure Appl. Math. 54, No. 4, 1145--1157 (2023; Zbl 07778481) Full Text: DOI
Elkies, Noam D.; Goel, Gaurav On powerful integers expressible as sums of two coprime fourth powers. (English) Zbl 07771756 Res. Number Theory 9, No. 4, Paper No. 78, 17 p. (2023). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G05 14H52 11D41 11G30 PDFBibTeX XMLCite \textit{N. D. Elkies} and \textit{G. Goel}, Res. Number Theory 9, No. 4, Paper No. 78, 17 p. (2023; Zbl 07771756) Full Text: DOI
Bennett, Michael A. Powers from products of terms in progressions with gaps. (English) Zbl 07771573 Acta Arith. 210, 205-222 (2023). MSC: 11D41 11G05 PDFBibTeX XMLCite \textit{M. A. Bennett}, Acta Arith. 210, 205--222 (2023; Zbl 07771573) Full Text: DOI
Mocanu, Diana Asymptotic Fermat for signatures \((r,r,p)\) using the modular approach. (English) Zbl 07754306 Res. Number Theory 9, No. 4, Paper No. 71, 17 p. (2023). Reviewer: Wataru Takeda (Tōkyō) MSC: 11D41 11G05 11F80 PDFBibTeX XMLCite \textit{D. Mocanu}, Res. Number Theory 9, No. 4, Paper No. 71, 17 p. (2023; Zbl 07754306) Full Text: DOI arXiv OA License
Grechuk, Bogdan; Grechuk, Tetiana; Wilcox, Ashleigh Diophantine equations with three monomials. (English) Zbl 07734967 J. Number Theory 253, 69-108 (2023). MSC: 11D41 PDFBibTeX XMLCite \textit{B. Grechuk} et al., J. Number Theory 253, 69--108 (2023; Zbl 07734967) Full Text: DOI arXiv
Eyidoğan, Sadık; Göral, Haydar; Kutlu, Mustafa Kutay Arithmetic progressions in certain subsets of finite fields. (English) Zbl 07732851 Finite Fields Appl. 91, Article ID 102264, 58 p. (2023). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11B25 11T24 PDFBibTeX XMLCite \textit{S. Eyidoğan} et al., Finite Fields Appl. 91, Article ID 102264, 58 p. (2023; Zbl 07732851) Full Text: DOI
Dujella, Andrej; Győry, Kálmán; Michaud-Jacobs, Philippe; Pintér, Ákos On power values of pyramidal numbers. II. (English) Zbl 07732767 Acta Arith. 208, No. 3, 199-213 (2023). MSC: 11D41 11D59 11D61 14G99 PDFBibTeX XMLCite \textit{A. Dujella} et al., Acta Arith. 208, No. 3, 199--213 (2023; Zbl 07732767) Full Text: DOI arXiv
Çam Çelik, Şermin; Eyidoğan, Sadık; Göral, Haydar; Sertbaş, Doğa Can On classification of sequences containing arbitrarily long arithmetic progressions. (English) Zbl 07730400 Int. J. Number Theory 19, No. 8, 1917-1952 (2023). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11B25 PDFBibTeX XMLCite \textit{Ş. Çam Çelik} et al., Int. J. Number Theory 19, No. 8, 1917--1952 (2023; Zbl 07730400) Full Text: DOI
Das, Pranabesh; Laishram, Shanta; Saradha, N.; Sharma, Divyum Rational solutions to the variants of Erdős-Selfridge superelliptic curves. (English) Zbl 07720859 Int. J. Number Theory 19, No. 7, 1707-1744 (2023). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D61 11D41 11Y50 11G05 PDFBibTeX XMLCite \textit{P. Das} et al., Int. J. Number Theory 19, No. 7, 1707--1744 (2023; Zbl 07720859) Full Text: DOI arXiv
Mocanu, Diana Asymptotic Fermat for signatures \((p,p,2)\) and \((p,p,3)\) over totally real fields. (English) Zbl 07740367 Mathematika 68, No. 4, 1233-1257 (2022). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D41 11R80 11Y40 PDFBibTeX XMLCite \textit{D. Mocanu}, Mathematika 68, No. 4, 1233--1257 (2022; Zbl 07740367) Full Text: DOI arXiv OA License
Michaud-Jacobs, Philippe On some generalized Fermat equations of the form \(x^2+y^{2n} = z^p\). (English) Zbl 07738298 Mathematika 68, No. 2, 344-361 (2022). MSC: 11D41 11F41 11F80 11G05 PDFBibTeX XMLCite \textit{P. Michaud-Jacobs}, Mathematika 68, No. 2, 344--361 (2022; Zbl 07738298) Full Text: DOI arXiv OA License
Antony, Deepa; Barman, Rupam; Chattopadhyay, Jaitra On denseness of certain direction and generalized direction sets. (English) Zbl 1507.11012 Integers 22, Paper A88, 9 p. (2022). Reviewer: Florian Luca (Johannesburg) MSC: 11B05 PDFBibTeX XMLCite \textit{D. Antony} et al., Integers 22, Paper A88, 9 p. (2022; Zbl 1507.11012) Full Text: arXiv Link
Pacetti, Ariel; Villagra Torcomian, Lucas \(\mathbb{Q}\)-curves, Hecke characters and some Diophantine equations. (English) Zbl 1503.11072 Math. Comput. 91, No. 338, 2817-2865 (2022). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D41 11F80 PDFBibTeX XMLCite \textit{A. Pacetti} and \textit{L. Villagra Torcomian}, Math. Comput. 91, No. 338, 2817--2865 (2022; Zbl 1503.11072) Full Text: DOI arXiv
Panraksa, Chatchawan Rational periodic points of \(x^d+c\) and Fermat-Catalan equations. (English) Zbl 1506.37121 Int. J. Number Theory 18, No. 5, 1111-1129 (2022). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 37P35 37P15 37P05 11C08 11D25 PDFBibTeX XMLCite \textit{C. Panraksa}, Int. J. Number Theory 18, No. 5, 1111--1129 (2022; Zbl 1506.37121) Full Text: DOI arXiv
Makhul, Mehdi; Roche-Newton, Oliver; Stevens, Sophie; Warren, Audie The Elekes-Szabó problem and the uniformity conjecture. (English) Zbl 1493.52017 Isr. J. Math. 248, No. 1, 39-66 (2022). MSC: 52C10 05A16 05D99 05C35 PDFBibTeX XMLCite \textit{M. Makhul} et al., Isr. J. Math. 248, No. 1, 39--66 (2022; Zbl 1493.52017) Full Text: DOI arXiv
Bennett, Michael A.; Gherga, Adela; Patel, Vandita; Siksek, Samir Odd values of the Ramanujan tau function. (English) Zbl 1525.11034 Math. Ann. 382, No. 1-2, 203-238 (2022). MSC: 11D61 11D41 11F80 11F41 PDFBibTeX XMLCite \textit{M. A. Bennett} et al., Math. Ann. 382, No. 1--2, 203--238 (2022; Zbl 1525.11034) Full Text: DOI arXiv
Fraser, Jonathan M.; Yu, Han Approximate arithmetic structure in large sets of integers. (English) Zbl 1484.11038 Real Anal. Exch. 46, No. 1, 163-174 (2021). Reviewer: Peter Massopust (München) MSC: 11B25 11B05 PDFBibTeX XMLCite \textit{J. M. Fraser} and \textit{H. Yu}, Real Anal. Exch. 46, No. 1, 163--174 (2021; Zbl 1484.11038) Full Text: DOI arXiv Link
Chałupka, Karolina Cubic forms, powers of primes and classification of elliptic curves. (English) Zbl 1490.11038 Colloq. Math. 166, No. 1, 137-150 (2021). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D41 11G05 PDFBibTeX XMLCite \textit{K. Chałupka}, Colloq. Math. 166, No. 1, 137--150 (2021; Zbl 1490.11038) Full Text: DOI
Dembner, Spencer; Jain, Vanshika Hyperelliptic curves and newform coefficients. (English) Zbl 1487.11064 J. Number Theory 225, 214-239 (2021). Reviewer: Francesc Bars Cortina (Bellaterra) MSC: 11G30 11F30 PDFBibTeX XMLCite \textit{S. Dembner} and \textit{V. Jain}, J. Number Theory 225, 214--239 (2021; Zbl 1487.11064) Full Text: DOI arXiv
Elsholtz, Christian Fermat’s last theorem implies Euclid’s infinitude of primes. (English) Zbl 1467.11008 Am. Math. Mon. 128, No. 3, 250-257 (2021). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11A41 05D10 11B75 PDFBibTeX XMLCite \textit{C. Elsholtz}, Am. Math. Mon. 128, No. 3, 250--257 (2021; Zbl 1467.11008) Full Text: DOI arXiv
Noubissie, Armand; Togbé, Alain On some ternary Diophantine equations of signature \((p,p,k)\). (English) Zbl 1483.11063 Bull. Malays. Math. Sci. Soc. (2) 44, No. 1, 163-170 (2021). MSC: 11D41 11D61 PDFBibTeX XMLCite \textit{A. Noubissie} and \textit{A. Togbé}, Bull. Malays. Math. Sci. Soc. (2) 44, No. 1, 163--170 (2021; Zbl 1483.11063) 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 1478.11040 Mediterr. J. Math. 18, No. 2, Paper No. 48, 24 p. (2021). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D41 11F33 11F80 11G05 11D61 11R18 PDFBibTeX XMLCite \textit{L. Dieulefait} and \textit{E. Soto}, Mediterr. J. Math. 18, No. 2, Paper No. 48, 24 p. (2021; Zbl 1478.11040) Full Text: DOI arXiv
Bennett, Michael A. Integers represented by \(x^4 - y^4\) revisited. (English) Zbl 1472.11096 Bull. Aust. Math. Soc. 103, No. 1, 38-49 (2021). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11D41 11F33 11F80 11G05 PDFBibTeX XMLCite \textit{M. A. Bennett}, Bull. Aust. Math. Soc. 103, No. 1, 38--49 (2021; Zbl 1472.11096) Full Text: DOI
Yan, Xiao-Hui The Diophantine equation \((m^2+n^2)^x+(2mn)^y=(m+n)^{2z}\). (English) Zbl 1472.11107 Int. J. Number Theory 16, No. 8, 1701-1708 (2020). Reviewer: Ilker Inam (Bilecik) MSC: 11D61 PDFBibTeX XMLCite \textit{X.-H. Yan}, Int. J. Number Theory 16, No. 8, 1701--1708 (2020; Zbl 1472.11107) 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 1478.11047 Honam Math. J. 42, No. 1, 139-150 (2020). MSC: 11D61 11J86 PDFBibTeX XMLCite \textit{E. Kizildere} and \textit{G. Soydan}, Honam Math. J. 42, No. 1, 139--150 (2020; Zbl 1478.11047) Full Text: DOI arXiv
Koutsianas, Angelos An application of the modular method and the symplectic argument to a Lebesgue-Nagell equation. (English) Zbl 1473.11077 Mathematika 66, No. 1, 230-244 (2020). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 PDFBibTeX XMLCite \textit{A. Koutsianas}, Mathematika 66, No. 1, 230--244 (2020; Zbl 1473.11077) Full Text: DOI arXiv
Ingram, Patrick Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. (English) Zbl 1456.37108 Int. Math. Res. Not. 2019, No. 15, 4859-4879 (2019). MSC: 37P05 37P30 11G50 PDFBibTeX XMLCite \textit{P. Ingram}, Int. Math. Res. Not. 2019, No. 15, 4859--4879 (2019; Zbl 1456.37108) Full Text: DOI arXiv
Billerey, Nicolas; Chen, Imin; Dieulefait, Luis; Freitas, Nuno A multi-Frey approach to Fermat equations of signature \((r,r,p)\). (English) Zbl 1446.11052 Trans. Am. Math. Soc. 371, No. 12, 8651-8677 (2019). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D41 11F80 11G05 PDFBibTeX XMLCite \textit{N. Billerey} et al., Trans. Am. Math. Soc. 371, No. 12, 8651--8677 (2019; Zbl 1446.11052) Full Text: DOI arXiv
Lemos, Pedro Some cases of Serre’s uniformity problem. (English) Zbl 1448.11107 Math. Z. 292, No. 1-2, 739-762 (2019). MSC: 11G05 PDFBibTeX XMLCite \textit{P. Lemos}, Math. Z. 292, No. 1--2, 739--762 (2019; Zbl 1448.11107) Full Text: DOI arXiv
Chen, Imin; Salari Sharif, Parinaz An explicit correspondence of modular curves. (English) Zbl 1484.11138 J. Number Theory 200, 185-204 (2019). Reviewer: Jordi Guárdia (Vilanova i la Geltrú) MSC: 11G18 14G35 PDFBibTeX XMLCite \textit{I. Chen} and \textit{P. Salari Sharif}, J. Number Theory 200, 185--204 (2019; Zbl 1484.11138) Full Text: DOI arXiv
Saito, Kota; Yoshida, Yuuya Arithmetic progressions in the graphs of slightly curved sequences. (English) Zbl 1407.11018 J. Integer Seq. 22, No. 2, Article 19.2.1, 25 p. (2019). MSC: 11B25 11B30 PDFBibTeX XMLCite \textit{K. Saito} and \textit{Y. Yoshida}, J. Integer Seq. 22, No. 2, Article 19.2.1, 25 p. (2019; Zbl 1407.11018) Full Text: arXiv Link
Zhang, Zhongfeng; Togbé, Alain Perfect powers that are sums of two powers of Fibonacci numbers. (English) Zbl 1465.11088 Bull. Aust. Math. Soc. 99, No. 1, 34-41 (2019). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11D61 11B39 PDFBibTeX XMLCite \textit{Z. Zhang} and \textit{A. Togbé}, Bull. Aust. Math. Soc. 99, No. 1, 34--41 (2019; Zbl 1465.11088) Full Text: DOI
Lemos, Pedro Serre’s uniformity conjecture for elliptic curves with rational cyclic isogenies. (English) Zbl 1461.11087 Trans. Am. Math. Soc. 371, No. 1, 137-146 (2019). MSC: 11G05 PDFBibTeX XMLCite \textit{P. Lemos}, Trans. Am. Math. Soc. 371, No. 1, 137--146 (2019; Zbl 1461.11087) Full Text: DOI arXiv
Yuan, Pingzhi; Han, Qing Jeśmanowicz’ conjecture and related equations. (English) Zbl 1410.11029 Acta Arith. 184, No. 1, 37-49 (2018). MSC: 11D61 11D41 PDFBibTeX XMLCite \textit{P. Yuan} and \textit{Q. Han}, Acta Arith. 184, No. 1, 37--49 (2018; Zbl 1410.11029) Full Text: DOI
Das, Pranabesh; Laishram, Shanta; Saradha, N. Variants of Erdős-Selfridge superelliptic curves and their rational points. (English) Zbl 1439.11151 Mathematika 64, No. 2, 380-386 (2018). MSC: 11G30 11D61 14G05 PDFBibTeX XMLCite \textit{P. Das} et al., Mathematika 64, No. 2, 380--386 (2018; Zbl 1439.11151) Full Text: DOI
Rebolledo, Marusia; Wuthrich, Christian A moduli interpretation for the non-split Cartan modular curve. (English) Zbl 1440.11106 Glasg. Math. J. 60, No. 2, 411-434 (2018). MSC: 11G18 11F80 14G35 14K10 PDFBibTeX XMLCite \textit{M. Rebolledo} and \textit{C. Wuthrich}, Glasg. Math. J. 60, No. 2, 411--434 (2018; Zbl 1440.11106) Full Text: DOI arXiv
Fraser, Jonathan M.; Yu, Han Arithmetic patches, weak tangents, and dimension. (English) Zbl 1429.11022 Bull. Lond. Math. Soc. 50, No. 1, 85-95 (2018). MSC: 11B25 28A80 11N13 PDFBibTeX XMLCite \textit{J. M. Fraser} and \textit{H. Yu}, Bull. Lond. Math. Soc. 50, No. 1, 85--95 (2018; Zbl 1429.11022) Full Text: DOI arXiv Link
Dąbrowski, Andrzej; Szymaszkiewicz, Lucjan Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves. (English) Zbl 1394.11057 Math. Comput. 87, No. 311, 1509-1522 (2018). Reviewer: Cyril Hugounenq (Grenoble) MSC: 11G40 11G05 11Y50 PDFBibTeX XMLCite \textit{A. Dąbrowski} and \textit{L. Szymaszkiewicz}, Math. Comput. 87, No. 311, 1509--1522 (2018; Zbl 1394.11057) Full Text: DOI arXiv
Kim, Dohyeong A modular approach to cubic Thue-Mahler equations. (English) Zbl 1407.11047 Math. Comput. 86, No. 305, 1435-1471 (2017). MSC: 11D59 11F11 11Y50 PDFBibTeX XMLCite \textit{D. Kim}, Math. Comput. 86, No. 305, 1435--1471 (2017; Zbl 1407.11047) Full Text: DOI arXiv Link
Bennett, Michael A.; Siksek, Samir Rational points on Erdős-Selfridge superelliptic curves. (English) Zbl 1407.11081 Compos. Math. 152, No. 11, 2249-2254 (2016). MSC: 11G30 11D61 11D41 11F80 PDFBibTeX XMLCite \textit{M. A. Bennett} and \textit{S. Siksek}, Compos. Math. 152, No. 11, 2249--2254 (2016; Zbl 1407.11081) Full Text: DOI arXiv
Bennett, Michael; Mihăilescu, Preda; Siksek, Samir The generalized Fermat equation. (English) Zbl 1440.11037 Nash, John Forbes jun. (ed.) et al., Open problems in mathematics. Cham: Springer. 173-205 (2016). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D41 11G05 14G05 14H25 PDFBibTeX XMLCite \textit{M. Bennett} et al., in: Open problems in mathematics. Cham: Springer. 173--205 (2016; Zbl 1440.11037) Full Text: DOI
Freitas, Nuno On the Fermat-type equation \(x^3+y^3=z^p\). (English) Zbl 1419.11058 Comment. Math. Helv. 91, No. 2, 295-304 (2016). MSC: 11D41 11G07 PDFBibTeX XMLCite \textit{N. Freitas}, Comment. Math. Helv. 91, No. 2, 295--304 (2016; Zbl 1419.11058) Full Text: DOI arXiv
Le Fourn, Samuel Surjectivity of Galois representations associated with quadratic \(\mathbb {Q}\)-curves. (English) Zbl 1342.11059 Math. Ann. 365, No. 1-2, 173-214 (2016). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11G10 11G16 11G18 PDFBibTeX XMLCite \textit{S. Le Fourn}, Math. Ann. 365, No. 1--2, 173--214 (2016; Zbl 1342.11059) Full Text: DOI arXiv
Hajdu, Lajos; Laishram, Shanta; Tengely, Szabolcs Power values of sums of products of consecutive integers. (English) Zbl 1400.11087 Acta Arith. 172, No. 4, 333-349 (2016). Reviewer: Volker Ziegler (Salzburg) MSC: 11D41 11D25 PDFBibTeX XMLCite \textit{L. Hajdu} et al., Acta Arith. 172, No. 4, 333--349 (2016; Zbl 1400.11087) Full Text: DOI Link
Miyazaki, T.; Terai, N. On Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. II. (English) Zbl 1374.11056 Acta Math. Hung. 147, No. 2, 286-293 (2015). Reviewer: Attila Bérczes (Debrecen) MSC: 11D61 11D41 PDFBibTeX XMLCite \textit{T. Miyazaki} and \textit{N. Terai}, Acta Math. Hung. 147, No. 2, 286--293 (2015; Zbl 1374.11056) Full Text: DOI
Dietmann, Rainer; Elsholtz, Christian Hilbert cubes in arithmetic sets. (English) Zbl 1342.11085 Rev. Mat. Iberoam. 31, No. 4, 1477-1498 (2015). Reviewer: Guoqing Wang (Tianjin) MSC: 11P70 11B75 11B25 11B30 11N36 PDFBibTeX XMLCite \textit{R. Dietmann} and \textit{C. Elsholtz}, Rev. Mat. Iberoam. 31, No. 4, 1477--1498 (2015; Zbl 1342.11085) Full Text: DOI arXiv
Freitas, Nuno Recipes to Fermat-type equations of the form \(x^r + y^r =Cz^p\). (English) Zbl 1369.11027 Math. Z. 279, No. 3-4, 605-639 (2015). MSC: 11D41 11G05 11F80 PDFBibTeX XMLCite \textit{N. Freitas}, Math. Z. 279, No. 3--4, 605--639 (2015; Zbl 1369.11027) Full Text: DOI arXiv
Silliman, Jesse; Vogt, Isabel Powers in Lucas sequences via Galois representations. (English) Zbl 1402.11028 Proc. Am. Math. Soc. 143, No. 3, 1027-1041 (2015). MSC: 11B39 11G05 PDFBibTeX XMLCite \textit{J. Silliman} and \textit{I. Vogt}, Proc. Am. Math. Soc. 143, No. 3, 1027--1041 (2015; Zbl 1402.11028) Full Text: DOI arXiv
Kortelainen, Juha On simple generators of recursively enumerable languages. (English) Zbl 1298.68144 J. Comput. Syst. Sci. 81, No. 1, 249-257 (2015). MSC: 68Q45 11D41 11D09 PDFBibTeX XMLCite \textit{J. Kortelainen}, J. Comput. Syst. Sci. 81, No. 1, 249--257 (2015; Zbl 1298.68144) Full Text: DOI
Terai, Nobuhiro On Jeśmanowicz’ conjecture concerning primitive Pythagorean triples. (English) Zbl 1309.11030 J. Number Theory 141, 316-323 (2014). MSC: 11D61 PDFBibTeX XMLCite \textit{N. Terai}, J. Number Theory 141, 316--323 (2014; Zbl 1309.11030) Full Text: DOI
Hajdu, Lajos; Pintér, Ákos; Tengely, Szabolcs; Varga, Nóra Equal values of figurate numbers. (English) Zbl 1383.11038 J. Number Theory 137, 130-141 (2014). MSC: 11D41 PDFBibTeX XMLCite \textit{L. Hajdu} et al., J. Number Theory 137, 130--141 (2014; Zbl 1383.11038) Full Text: DOI
Bennett, Michael A.; Dahmen, Sander R. Klein forms and the generalized superelliptic equation. (English) Zbl 1321.11059 Ann. Math. (2) 177, No. 1, 171-239 (2013). MSC: 11G05 11F80 11D25 11D59 PDFBibTeX XMLCite \textit{M. A. Bennett} and \textit{S. R. Dahmen}, Ann. Math. (2) 177, No. 1, 171--239 (2013; Zbl 1321.11059) Full Text: DOI
Győry, K.; Pintér, Á. Binomial Thue equations, ternary equations and power values of polynomials. (English. Russian original) Zbl 1354.11027 J. Math. Sci., New York 180, No. 5, 569-580 (2012); translation from Fundam. Prikl. Mat. 16, No. 5, 61-77 (2010). MSC: 11D61 11D59 PDFBibTeX XMLCite \textit{K. Győry} and \textit{Á. Pintér}, J. Math. Sci., New York 180, No. 5, 569--580 (2012; Zbl 1354.11027); translation from Fundam. Prikl. Mat. 16, No. 5, 61--77 (2010) Full Text: DOI Link
Dietmann, Rainer; Elsholtz, Christian Hilbert cubes in progression-free sets and in the set of squares. (English) Zbl 1347.11013 Isr. J. Math. 192, Part A, 59-66 (2012). MSC: 11B30 PDFBibTeX XMLCite \textit{R. Dietmann} and \textit{C. Elsholtz}, Isr. J. Math. 192, Part A, 59--66 (2012; Zbl 1347.11013) Full Text: DOI arXiv
Lukkassen, Dag; Høibakk, Ralph; Meidell, Annette Nonlinear laminates where the effective conductivity is integer valued. (English) Zbl 1241.80006 Appl. Math. Lett. 25, No. 6, 937-940 (2012). MSC: 80A20 PDFBibTeX XMLCite \textit{D. Lukkassen} et al., Appl. Math. Lett. 25, No. 6, 937--940 (2012; Zbl 1241.80006) Full Text: DOI
Reynolds, Jonathan Perfect powers in elliptic divisibility sequences. (English) Zbl 1276.11094 J. Number Theory 132, No. 5, 998-1015 (2012). MSC: 11G05 11D41 PDFBibTeX XMLCite \textit{J. Reynolds}, J. Number Theory 132, No. 5, 998--1015 (2012; Zbl 1276.11094) Full Text: DOI arXiv
Reynolds, Jonathan Perfect powers generated by the twisted Fermat cubic. (English) Zbl 1286.11092 Funct. Approximatio, Comment. Math. 46, No. 1, 133-145 (2012). MSC: 11G05 11D41 PDFBibTeX XMLCite \textit{J. Reynolds}, Funct. Approximatio, Comment. Math. 46, No. 1, 133--145 (2012; Zbl 1286.11092) Full Text: DOI arXiv Euclid
Xarles, Xavier Squares in arithmetic progression over number fields. (English) Zbl 1280.11037 J. Number Theory 132, No. 3, 379-389 (2012). Reviewer: Lajos Hajdu (Debrecen) MSC: 11G30 11B25 11D45 14H25 PDFBibTeX XMLCite \textit{X. Xarles}, J. Number Theory 132, No. 3, 379--389 (2012; Zbl 1280.11037) Full Text: DOI arXiv
Miyazaki, Takafumi Jeśmanowicz’ conjecture on exponential Diophantine equations. (English) Zbl 1266.11064 Funct. Approximatio, Comment. Math. 45, No. 2, 207-229 (2011). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D61 11D41 11J86 PDFBibTeX XMLCite \textit{T. Miyazaki}, Funct. Approximatio, Comment. Math. 45, No. 2, 207--229 (2011; Zbl 1266.11064) Full Text: DOI Euclid
Hajdu, L.; Kovács, T. Almost fifth powers in arithmetic progression. (English) Zbl 1253.11045 J. Number Theory 131, No. 10, 1912-1923 (2011). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D61 11B25 PDFBibTeX XMLCite \textit{L. Hajdu} and \textit{T. Kovács}, J. Number Theory 131, No. 10, 1912--1923 (2011; Zbl 1253.11045) Full Text: DOI
Laubenbacher, Reinhard; Pengelley, David “Voici ce que j’ai trouvé:” Sophie Germain’s grand plan to prove Fermat’s last theorem. (English) Zbl 1205.01010 Hist. Math. 37, No. 4, 641-692 (2010). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 01A50 01A55 11-03 11D41 PDFBibTeX XMLCite \textit{R. Laubenbacher} and \textit{D. Pengelley}, Hist. Math. 37, No. 4, 641--692 (2010; Zbl 1205.01010) Full Text: DOI arXiv
González-Jiménez, Enrique Three cubes in arithmetic progression over quadratic fields. (English) Zbl 1268.11015 Arch. Math. 95, No. 3, 233-241 (2010). MSC: 11B25 11G05 11R11 PDFBibTeX XMLCite \textit{E. González-Jiménez}, Arch. Math. 95, No. 3, 233--241 (2010; Zbl 1268.11015) Full Text: DOI arXiv
Siksek, Samir; Stoll, Michael On a problem of Hajdu and Tengely. (English) Zbl 1257.11033 Hanrot, Guillaume (ed.) et al., Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19–23, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-14517-9/pbk). Lecture Notes in Computer Science 6197, 316-330 (2010). MSC: 11D61 11Y50 PDFBibTeX XMLCite \textit{S. Siksek} and \textit{M. Stoll}, Lect. Notes Comput. Sci. 6197, 316--330 (2010; Zbl 1257.11033) Full Text: DOI arXiv
Hajdu, Lajos; Tengely, Szabolcs Arithmetic progressions of squares, cubes and \(n\)-th powers. (English) Zbl 1230.11040 Funct. Approximatio, Comment. Math. 41, No. 2, 129-138 (2009). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D61 11Y50 PDFBibTeX XMLCite \textit{L. Hajdu} and \textit{S. Tengely}, Funct. Approximatio, Comment. Math. 41, No. 2, 129--138 (2009; Zbl 1230.11040) Full Text: DOI arXiv Euclid
Chen, Imin; Siksek, Samir Perfect powers expressible as sums of two cubes. (English) Zbl 1215.11026 J. Algebra 322, No. 3, 638-656 (2009). Reviewer: Alain Kraus (Paris) MSC: 11D25 11D41 PDFBibTeX XMLCite \textit{I. Chen} and \textit{S. Siksek}, J. Algebra 322, No. 3, 638--656 (2009; Zbl 1215.11026) Full Text: DOI
Høibakk, Ralph; Lukkassen, Dag Power means with integer values. (English) Zbl 1271.11032 Elem. Math. 64, No. 3, 122-128 (2009). Reviewer: Florian Luca (Morelia) MSC: 11D09 11D41 PDFBibTeX XMLCite \textit{R. Høibakk} and \textit{D. Lukkassen}, Elem. Math. 64, No. 3, 122--128 (2009; Zbl 1271.11032) Full Text: DOI
Bugeaud, Yann; Luca, Florian; Mignotte, Maurice; Siksek, Samir Fibonacci numbers at most one away from a perfect power. (English) Zbl 1156.11008 Elem. Math. 63, No. 2, 65-75 (2008). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11B39 11D61 11G05 11J86 11Y50 PDFBibTeX XMLCite \textit{Y. Bugeaud} et al., Elem. Math. 63, No. 2, 65--75 (2008; Zbl 1156.11008) Full Text: DOI Link
Bennett, Michael A. The Diophantine equation \((x^{k} - 1)(y^{k} - 1) = (z^{k} - 1)^{t}\). (English) Zbl 1169.11015 Indag. Math., New Ser. 18, No. 4, 507-525 (2007). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D61 11J82 11J86 11D45 PDFBibTeX XMLCite \textit{M. A. Bennett}, Indag. Math., New Ser. 18, No. 4, 507--525 (2007; Zbl 1169.11015) Full Text: DOI
Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael Twists of \(X(7)\) and primitive solutions to \(x^2+y^3=z^7\). (English) Zbl 1124.11019 Duke Math. J. 137, No. 1, 103-158 (2007). Reviewer: Alain Kraus (Paris) MSC: 11D41 11G10 11G18 11G30 14G05 PDFBibTeX XMLCite \textit{B. Poonen} et al., Duke Math. J. 137, No. 1, 103--158 (2007; Zbl 1124.11019) Full Text: DOI arXiv
Bruin, N.; Győry, K.; Hajdu, L.; Tengely, Sz. Arithmetic progressions consisting of unlike powers. (English) Zbl 1142.11018 Indag. Math., New Ser. 17, No. 4, 539-555 (2006). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11B25 11G30 11Y50 PDFBibTeX XMLCite \textit{N. Bruin} et al., Indag. Math., New Ser. 17, No. 4, 539--555 (2006; Zbl 1142.11018) Full Text: DOI arXiv
Luca, Florian; Szalay, László Congruent numbers with higher exponents. (English) Zbl 1138.11010 Acta Math. Univ. Ostrav. 14, No. 1, 49-55 (2006). Reviewer: Gábor Nyul (Debrecen) MSC: 11D41 11D25 PDFBibTeX XMLCite \textit{F. Luca} and \textit{L. Szalay}, Acta Math. Univ. Ostrav. 14, No. 1, 49--55 (2006; Zbl 1138.11010) Full Text: EuDML
Bennett, Michael A. The equation \(x^{2n}+y^{2n}=z^5\). (English) Zbl 1138.11009 J. Théor. Nombres Bordx. 18, No. 2, 315-321 (2006). Reviewer: Alain Kraus (Paris) MSC: 11D41 PDFBibTeX XMLCite \textit{M. A. Bennett}, J. Théor. Nombres Bordx. 18, No. 2, 315--321 (2006; Zbl 1138.11009) Full Text: DOI Numdam EuDML
Bars, Francesc; Dieulefait, Luis Galois actions on \(Q\)-curves and winding quotients. (English) Zbl 1196.11075 Math. Z. 254, No. 3, 531-538 (2006). MSC: 11F80 11G05 11G18 PDFBibTeX XMLCite \textit{F. Bars} and \textit{L. Dieulefait}, Math. Z. 254, No. 3, 531--538 (2006; Zbl 1196.11075) Full Text: DOI arXiv
Le, Maohua A conjecture concerning the pure exponential Diophantine equation \(a^x+b^y= c^z\). (English) Zbl 1159.11308 Acta Math. Sin., Engl. Ser. 21, No. 4, 943-948 (2005). MSC: 11D61 PDFBibTeX XMLCite \textit{M. Le}, Acta Math. Sin., Engl. Ser. 21, No. 4, 943--948 (2005; Zbl 1159.11308) Full Text: DOI
Bennett, Michael A. Powers in recurrence sequences: Pell equations. (English) Zbl 1125.11019 Trans. Am. Math. Soc. 357, No. 4, 1675-1691 (2005). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11D45 11B37 PDFBibTeX XMLCite \textit{M. A. Bennett}, Trans. Am. Math. Soc. 357, No. 4, 1675--1691 (2005; Zbl 1125.11019) Full Text: DOI
Bugeaud, Yann On the Diophantine equation \((x^ k-1)(y^ k-1)=(z^ k-1)\). (English) Zbl 1098.11022 Indag. Math., New Ser. 15, No. 1, 21-28 (2004). Reviewer: Kálmán Liptai (Eger) MSC: 11D61 11J86 PDFBibTeX XMLCite \textit{Y. Bugeaud}, Indag. Math., New Ser. 15, No. 1, 21--28 (2004; Zbl 1098.11022) Full Text: DOI
Siksek, Samir On the Diophantine equation \(x^2= y^p+2^kz^p\). (English) Zbl 1074.11022 J. Théor. Nombres Bordx. 15, No. 3, 839-846 (2003). Reviewer: Edward L. Cohen (Ottawa) MSC: 11D61 PDFBibTeX XMLCite \textit{S. Siksek}, J. Théor. Nombres Bordx. 15, No. 3, 839--846 (2003; Zbl 1074.11022) Full Text: DOI Numdam EuDML
Sitaraman, Sankar Note on a Fermat-type Diophantine equation. (English) Zbl 1027.11023 J. Number Theory 99, No. 1, 29-35 (2003). Reviewer: Tauno Metsänkylä (Turku) MSC: 11D41 11R18 PDFBibTeX XMLCite \textit{S. Sitaraman}, J. Number Theory 99, No. 1, 29--35 (2003; Zbl 1027.11023) Full Text: DOI
Terai, Nobuhiro On the Diophantine equations \(\binom n2=cx^l\) and \(\binom n3=cx^l\). (English) Zbl 1040.11016 Tokyo J. Math. 25, No. 2, 209-220 (2002). Reviewer: Kálmán Liptai (Eger) MSC: 11D61 11D59 PDFBibTeX XMLCite \textit{N. Terai}, Tokyo J. Math. 25, No. 2, 209--220 (2002; Zbl 1040.11016) Full Text: DOI
Luca, F.; Walsh, P. G. The product of like-indexed terms in binary recurrences. (English) Zbl 1018.11015 J. Number Theory 96, No. 1, 152-173 (2002). Reviewer: Roelof J.Stroeker (Rotterdam) MSC: 11D61 11B37 PDFBibTeX XMLCite \textit{F. Luca} and \textit{P. G. Walsh}, J. Number Theory 96, No. 1, 152--173 (2002; Zbl 1018.11015) Full Text: DOI
Flammenkamp, Achim; Luca, Florian Binomial coefficients and Lucas sequences. (English) Zbl 0995.11011 J. Number Theory 93, No. 2, 246-284 (2002). Reviewer: N.Robbins (San Francisco) MSC: 11B65 11D99 11B39 PDFBibTeX XMLCite \textit{A. Flammenkamp} and \textit{F. Luca}, J. Number Theory 93, No. 2, 246--284 (2002; Zbl 0995.11011) Full Text: DOI
Chen, Imin On relations between Jacobians of certain modular curves. (English) Zbl 0990.14012 J. Algebra 231, No. 1, 414-448 (2000). Reviewer: Ch.Birkenhake (Erlangen) MSC: 14H40 14G35 14H10 PDFBibTeX XMLCite \textit{I. Chen}, J. Algebra 231, No. 1, 414--448 (2000; Zbl 0990.14012) Full Text: DOI arXiv
Darmon, Henri Rigid local systems, Hilbert modular forms, and Fermat’s last theorem. (English) Zbl 1008.11023 Duke Math. J. 102, No. 3, 413-449 (2000). Reviewer: Michael Stoll (Bremen) MSC: 11G18 11F80 11D41 11G05 PDFBibTeX XMLCite \textit{H. Darmon}, Duke Math. J. 102, No. 3, 413--449 (2000; Zbl 1008.11023) Full Text: DOI
Sitaraman, Sankar On a Fermat-type Diophantine equation. (English) Zbl 0972.11015 J. Number Theory 80, No. 2, 174-186 (2000). Reviewer: Tauno Metsänkylä (Turku) MSC: 11D41 11R18 PDFBibTeX XMLCite \textit{S. Sitaraman}, J. Number Theory 80, No. 2, 174--186 (2000; Zbl 0972.11015) Full Text: DOI Link
Merel, Loïc Arithmetic of elliptic curves and diophantine equations. (English) Zbl 0964.11028 J. Théor. Nombres Bordx. 11, No. 1, 173-200 (1999). Reviewer: D.Poulakis (Thessaloniki) MSC: 11G05 11D41 PDFBibTeX XMLCite \textit{L. Merel}, J. Théor. Nombres Bordx. 11, No. 1, 173--200 (1999; Zbl 0964.11028) Full Text: DOI Numdam EuDML EMIS
Beukers, Frits The Diophantine equation \(Ax^ p+By^ q=Cz^ r\). (English) Zbl 1038.11505 Duke Math. J. 91, No. 1, 61-88 (1998). Reviewer: Andrew Granville (MR 99f:11039) MSC: 11D41 20H10 PDFBibTeX XMLCite \textit{F. Beukers}, Duke Math. J. 91, No. 1, 61--88 (1998; Zbl 1038.11505) Full Text: DOI
Bennett, Michael A.; de Weger, Benjamin M. M. On the diophantine equation \(| ax^n-by^n|=1\). (English) Zbl 0892.11041 Math. Comput. 67, No. 221, 413-438 (1998). Reviewer: Nigel Smart (Bristol) MSC: 11Y50 11D41 PDFBibTeX XMLCite \textit{M. A. Bennett} and \textit{B. M. M. de Weger}, Math. Comput. 67, No. 221, 413--438 (1998; Zbl 0892.11041) Full Text: DOI