Andrica, Dorin; Ţurcaş, George C. Pairs of rational triangles with equal symmetric invariants. (English) Zbl 1453.14072 J. Number Theory 221, 496-504 (2021). MSC: 14G05 11G30 11Y50 PDF BibTeX XML Cite \textit{D. Andrica} and \textit{G. C. Ţurcaş}, J. Number Theory 221, 496--504 (2021; Zbl 1453.14072) 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
Demark, David; Hindes, Wade; Jones, Rafe; Misplon, Moses; Stoll, Michael; Stoneman, Michael Eventually stable quadratic polynomials over \(\mathbb{Q}\). (English) Zbl 1446.37100 New York J. Math. 26, 526-561 (2020). Reviewer: Artūras Dubickas (Vilnius) MSC: 37P15 11R09 37P05 12E05 11R32 11R45 PDF BibTeX XML Cite \textit{D. Demark} et al., New York J. Math. 26, 526--561 (2020; Zbl 1446.37100) Full Text: Link
Stoll, Michael Diagonal genus 5 curves, elliptic curves over \(\mathbb{Q}(t)\), and rational Diophantine quintuples. (English) Zbl 07118296 Acta Arith. 190, No. 3, 239-261 (2019). MSC: 11D09 11G05 11G30 14G05 14H40 11Y50 14G25 14G27 14H25 14H52 PDF BibTeX XML Cite \textit{M. Stoll}, Acta Arith. 190, No. 3, 239--261 (2019; Zbl 07118296) Full Text: DOI
Balakrishnan, Jennifer; Dogra, Netan; Müller, J. Steffen; Tuitman, Jan; Vonk, Jan Explicit Chabauty-Kim for the split Cartan modular curve of level 13. (English) Zbl 07097493 Ann. Math. (2) 189, No. 3, 885-944 (2019). MSC: 14G05 11Y50 11G50 11G18 PDF BibTeX XML Cite \textit{J. Balakrishnan} et al., Ann. Math. (2) 189, No. 3, 885--944 (2019; Zbl 07097493) Full Text: DOI
Morrow, Jackson S. Composite images of Galois for elliptic curves over \(\mathbb {Q}\) and entanglement fields. (English) Zbl 07066485 Math. Comput. 88, No. 319, 2389-2421 (2019). MSC: 11G05 11D45 11G18 11F80 PDF BibTeX XML Cite \textit{J. S. Morrow}, Math. Comput. 88, No. 319, 2389--2421 (2019; Zbl 07066485) Full Text: DOI
Tengely, Szabolcs; Ulas, Maciej Power values of sums of certain products of consecutive integers and related results. (English) Zbl 1450.11025 J. Number Theory 197, 341-360 (2019). Reviewer: Florian Luca (Johannesburg) MSC: 11D41 PDF BibTeX XML Cite \textit{S. Tengely} and \textit{M. Ulas}, J. Number Theory 197, 341--360 (2019; Zbl 1450.11025) Full Text: DOI arXiv
Miyazaki, Takafumi Contributions to some conjectures on a ternary exponential Diophantine equation. (English) Zbl 1428.11062 Acta Arith. 186, No. 1, 1-36 (2018). Reviewer: Florian Luca (Johannesburg) MSC: 11D61 11J86 11D41 PDF BibTeX XML Cite \textit{T. Miyazaki}, Acta Arith. 186, No. 1, 1--36 (2018; Zbl 1428.11062) Full Text: DOI
Goedhart, Eva G.; Grundman, Helen G. On the Diophantine equation \(X^{2N}+2^{2\alpha}5^{2\beta}p^{2\gamma}=Z^5\). (English) Zbl 1413.11071 Period. Math. Hung. 75, No. 2, 196-200 (2017). MSC: 11D45 PDF BibTeX XML Cite \textit{E. G. Goedhart} and \textit{H. G. Grundman}, Period. Math. Hung. 75, No. 2, 196--200 (2017; Zbl 1413.11071) Full Text: DOI arXiv
Patsolic, Jesse; Rouse, Jeremy Trinomials defining quintic number fields. (English) Zbl 1388.11035 Int. J. Number Theory 13, No. 7, 1881-1894 (2017). Reviewer: Shabnam Akhtari (Eugene) MSC: 11G30 11D41 11G05 PDF BibTeX XML Cite \textit{J. Patsolic} and \textit{J. Rouse}, Int. J. Number Theory 13, No. 7, 1881--1894 (2017; Zbl 1388.11035) Full Text: DOI arXiv
Balakrishnan, Jennifer S.; Besser, Amnon; Müller, J. Steffen Computing integral points on hyperelliptic curves using quadratic Chabauty. (English) Zbl 1376.11053 Math. Comput. 86, No. 305, 1403-1434 (2017). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11S80 11Y50 14G40 PDF BibTeX XML Cite \textit{J. S. Balakrishnan} et al., Math. Comput. 86, No. 305, 1403--1434 (2017; Zbl 1376.11053) Full Text: DOI
Rouse, Jeremy; Zureick-Brown, David Elliptic curves over \(\mathbb {Q}\) and 2-adic images of Galois. (English) Zbl 1397.11095 Res. Number Theory 1, Paper No. 12, 34 p. (2015). Reviewer: Olaf Ninnemann (Uffing am Staffelsee) MSC: 11G05 11F80 11G18 PDF BibTeX XML Cite \textit{J. Rouse} and \textit{D. Zureick-Brown}, Res. Number Theory 1, Paper No. 12, 34 p. (2015; Zbl 1397.11095) Full Text: DOI arXiv
Miyazaki, Takafumi Upper bounds for solutions of an exponential Diophantine equation. (English) Zbl 1378.11046 Rocky Mt. J. Math. 45, No. 1, 303-344 (2015). MSC: 11D61 11D41 PDF BibTeX XML Cite \textit{T. Miyazaki}, Rocky Mt. J. Math. 45, No. 1, 303--344 (2015; Zbl 1378.11046) Full Text: DOI Euclid
Flynn, E. V.; Testa, D. Finite Weil restriction of curves. (English) Zbl 1319.11040 Monatsh. Math. 176, No. 2, 197-218 (2015). Reviewer: Szabolcs Tengely (Debrecen) MSC: 11G30 11G10 14H40 PDF BibTeX XML Cite \textit{E. V. Flynn} and \textit{D. Testa}, Monatsh. Math. 176, No. 2, 197--218 (2015; Zbl 1319.11040) Full Text: DOI arXiv
González-Jiménez, Enrique On arithmetic progressions on Edwards curves. (English) Zbl 1322.11057 Acta Arith. 167, No. 2, 117-132 (2015). Reviewer: Michael Th. Rassias (Princeton) MSC: 11G05 11G30 11B25 11D45 14G05 PDF BibTeX XML Cite \textit{E. González-Jiménez}, Acta Arith. 167, No. 2, 117--132 (2015; Zbl 1322.11057) Full Text: DOI arXiv
Bennett, Michael A.; Chen, Imin; Dahmen, Sander R.; Yazdani, Soroosh Generalized Fermat equations: a miscellany. (English) Zbl 1390.11065 Int. J. Number Theory 11, No. 1, 1-28 (2015). MSC: 11D41 11D61 11G05 14G05 PDF BibTeX XML Cite \textit{M. A. Bennett} et al., Int. J. Number Theory 11, No. 1, 1--28 (2015; Zbl 1390.11065) Full Text: DOI
Siksek, Samir; Stoll, Michael The generalised Fermat equation \(x^{2} + y^{3} = z^{15}\). (English) Zbl 1303.11074 Arch. Math. 102, No. 5, 411-421 (2014). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G35 14K20 PDF BibTeX XML Cite \textit{S. Siksek} and \textit{M. Stoll}, Arch. Math. 102, No. 5, 411--421 (2014; Zbl 1303.11074) Full Text: DOI arXiv
Mourao, Michael Extending elliptic curve Chabauty to higher genus curves. (English) Zbl 1377.11078 Manuscr. Math. 143, No. 3-4, 355-377 (2014). MSC: 11G30 11D41 14H25 PDF BibTeX XML Cite \textit{M. Mourao}, Manuscr. Math. 143, No. 3--4, 355--377 (2014; Zbl 1377.11078) Full Text: DOI arXiv
González-Jiménez, Enrique; Xarles, Xavier Five squares in arithmetic progression over quadratic fields. (English) Zbl 1362.11013 Rev. Mat. Iberoam. 29, No. 4, 1211-1238 (2013). MSC: 11B25 11N36 11G30 14H25 PDF BibTeX XML Cite \textit{E. González-Jiménez} and \textit{X. Xarles}, Rev. Mat. Iberoam. 29, No. 4, 1211--1238 (2013; Zbl 1362.11013) Full Text: DOI arXiv
Brown, Stephen C.; Spearman, Blair K.; Yang, Qiduan On sextic trinomials with Galois group \(C_6, S_3\) or \(C_3 \times S_3\). (English) Zbl 1290.12005 J. Algebra Appl. 12, No. 1, Paper No. 1250128, 9 p. (2013). MSC: 12F10 11G30 12E05 PDF BibTeX XML Cite \textit{S. C. Brown} et al., J. Algebra Appl. 12, No. 1, Paper No. 1250128, 9 p. (2013; Zbl 1290.12005) Full Text: DOI
Stoll, Michael Rational points on curves. (English. French summary) Zbl 1270.11030 J. Théor. Nombres Bordx. 23, No. 1, 257-277 (2011). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D41 11G30 14G05 14G25 PDF BibTeX XML Cite \textit{M. Stoll}, J. Théor. Nombres Bordx. 23, No. 1, 257--277 (2011; Zbl 1270.11030) Full Text: DOI EuDML 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 PDF BibTeX XML Cite \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 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{T. Kovács}, J. Number Theory 131, No. 10, 1912--1923 (2011; Zbl 1253.11045) Full Text: DOI
Bruin, Nils; Stoll, Michael Two-cover descent on hyperelliptic curves. (English) Zbl 1208.11078 Math. Comput. 78, No. 268, 2347-2370 (2009). Reviewer: Takao Yamazaki (Tohoku) MSC: 11G30 11Y50 14H40 PDF BibTeX XML Cite \textit{N. Bruin} and \textit{M. Stoll}, Math. Comput. 78, No. 268, 2347--2370 (2009; Zbl 1208.11078) 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 PDF BibTeX XML Cite \textit{L. Hajdu} and \textit{S. Tengely}, Funct. Approximatio, Comment. Math. 41, No. 2, 129--138 (2009; Zbl 1230.11040) Full Text: DOI Euclid arXiv
Ghioca, Dragos; Tucker, T. J. Periodic points, linearizing maps, and the dynamical Mordell-Lang problem. (English) Zbl 1186.14047 J. Number Theory 129, No. 6, 1392-1403 (2009). Reviewer: Jorge Pineiro (Bronx) MSC: 14K12 37P35 37P20 14C25 PDF BibTeX XML Cite \textit{D. Ghioca} and \textit{T. J. Tucker}, J. Number Theory 129, No. 6, 1392--1403 (2009; Zbl 1186.14047) Full Text: DOI arXiv
Hajdu, L. Powerful arithmetic progressions. (English) Zbl 1186.11017 Indag. Math., New Ser. 19, No. 4, 547-561 (2008). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D61 11B25 11Y50 PDF BibTeX XML Cite \textit{L. Hajdu}, Indag. Math., New Ser. 19, No. 4, 547--561 (2008; Zbl 1186.11017) Full Text: DOI
Bremner, A.; Tzanakis, N. On squares in Lucas sequences. (English) Zbl 1124.11013 J. Number Theory 124, No. 2, 511-520 (2007). Reviewer: Alain Kraus (Paris) MSC: 11B39 PDF BibTeX XML Cite \textit{A. Bremner} and \textit{N. Tzanakis}, J. Number Theory 124, No. 2, 511--520 (2007; Zbl 1124.11013) Full Text: DOI arXiv
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 PDF BibTeX XML Cite \textit{B. Poonen} et al., Duke Math. J. 137, No. 1, 103--158 (2007; Zbl 1124.11019) Full Text: DOI arXiv
Bruin, Nils The primitive solutions to \(x^3+y^9=z^2\). (English) Zbl 1081.11019 J. Number Theory 111, No. 1, 179-189 (2005). Reviewer: D. Poulakis (Thessaloniki) MSC: 11D41 11D72 11G35 14H25 PDF BibTeX XML Cite \textit{N. Bruin}, J. Number Theory 111, No. 1, 179--189 (2005; Zbl 1081.11019) Full Text: DOI arXiv
Bruin, Nils; Flynn, E. Victor Towers of 2-covers of hyperelliptic curves. (English) Zbl 1145.11317 Trans. Am. Math. Soc. 357, No. 11, 4329-4347 (2005). MSC: 11G30 11G10 14H40 PDF BibTeX XML Cite \textit{N. Bruin} and \textit{E. V. Flynn}, Trans. Am. Math. Soc. 357, No. 11, 4329--4347 (2005; Zbl 1145.11317) Full Text: DOI
Flynn, E. V. The Hasse principle and the Brauer-Manin obstruction for curves. (English) Zbl 1069.11023 Manuscr. Math. 115, No. 4, 437-466 (2004). Reviewer: M. Rafiq Omar (Bellville) MSC: 11G30 11G10 14H40 14H25 14G05 PDF BibTeX XML Cite \textit{E. V. Flynn}, Manuscr. Math. 115, No. 4, 437--466 (2004; Zbl 1069.11023) Full Text: DOI
Bremner, A.; Tzanakis, N. Lucas sequences whose 12th or 9th term is a square. (English) Zbl 1059.11015 J. Number Theory 107, No. 2, 215-227 (2004). Reviewer: Alain Kraus (Paris) MSC: 11B39 11G05 PDF BibTeX XML Cite \textit{A. Bremner} and \textit{N. Tzanakis}, J. Number Theory 107, No. 2, 215--227 (2004; Zbl 1059.11015) Full Text: DOI
Bruin, Nils Chabauty methods using elliptic curves. (English) Zbl 1135.11320 J. Reine Angew. Math. 562, 27-49 (2003). MSC: 11G05 14G05 PDF BibTeX XML Cite \textit{N. Bruin}, J. Reine Angew. Math. 562, 27--49 (2003; Zbl 1135.11320) Full Text: DOI
Flynn, E. V.; Redmond, J. Application of covering techniques to families of curves. (English) Zbl 1119.14026 J. Number Theory 101, No. 2, 376-397 (2003). MSC: 14H30 11G30 11G10 14H40 14G05 PDF BibTeX XML Cite \textit{E. V. Flynn} and \textit{J. Redmond}, J. Number Theory 101, No. 2, 376--397 (2003; Zbl 1119.14026) Full Text: DOI