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
Hasanalizade, Elchin On near-perfect numbers of special forms. (English) Zbl 07764663 Bull. Aust. Math. Soc. 108, No. 3, 366-372 (2023). MSC: 11A25 11B39 PDFBibTeX XMLCite \textit{E. Hasanalizade}, Bull. Aust. Math. Soc. 108, No. 3, 366--372 (2023; Zbl 07764663) Full Text: DOI arXiv OA License
Anitha, K.; Mumtaj Fathima, I.; Vijayalakshmi, A. R. Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture. (English) Zbl 07738914 Open Math. 21, Article ID 20220563, 9 p. (2023). MSC: 11A41 11N13 11B39 PDFBibTeX XMLCite \textit{K. Anitha} et al., Open Math. 21, Article ID 20220563, 9 p. (2023; Zbl 07738914) Full Text: DOI arXiv
Chan, Tsz Ho A note on powerful numbers in short intervals. (English) Zbl 07734857 Bull. Aust. Math. Soc. 108, No. 1, 99-106 (2023). Reviewer: Florian Luca (Johannesburg) MSC: 11N25 PDFBibTeX XMLCite \textit{T. H. Chan}, Bull. Aust. Math. Soc. 108, No. 1, 99--106 (2023; Zbl 07734857) Full Text: DOI arXiv
Barrios, Alexander J. Lower bounds for the modified Szpiro ratio. (English) Zbl 07732759 Acta Arith. 208, No. 1, 51-68 (2023). MSC: 11G05 11D75 11J25 PDFBibTeX XMLCite \textit{A. J. Barrios}, Acta Arith. 208, No. 1, 51--68 (2023; Zbl 07732759) Full Text: DOI arXiv
Balaji, Nikhil; Luca, Florian Terms of Lucas sequences having a large smooth divisor. (English) Zbl 1527.11009 Can. Math. Bull. 66, No. 1, 225-231 (2023). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B39 11B37 11B65 PDFBibTeX XMLCite \textit{N. Balaji} and \textit{F. Luca}, Can. Math. Bull. 66, No. 1, 225--231 (2023; Zbl 1527.11009) Full Text: DOI arXiv
Chan, Tsz Ho Arithmetic progressions among powerful numbers. (English) Zbl 1515.11089 J. Integer Seq. 26, No. 1, Article 23.1.1, 10 p. (2023). Reviewer: Giovanni Coppola (Napoli) MSC: 11N25 11D41 11A05 11B25 PDFBibTeX XMLCite \textit{T. H. Chan}, J. Integer Seq. 26, No. 1, Article 23.1.1, 10 p. (2023; Zbl 1515.11089) Full Text: arXiv Link
Barrios, Alexander J. Good elliptic curves with a specified torsion subgroup. (English) Zbl 1505.11085 J. Number Theory 242, 21-43 (2023). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11D75 11J25 PDFBibTeX XMLCite \textit{A. J. Barrios}, J. Number Theory 242, 21--43 (2023; Zbl 1505.11085) Full Text: DOI arXiv
Pasten, Hector Arithmetic derivatives through geometry of numbers. (English) Zbl 1523.11134 Can. Math. Bull. 65, No. 4, 906-923 (2022). Reviewer: Oleg Karpenkov (Liverpool) MSC: 11J97 11H06 14A23 PDFBibTeX XMLCite \textit{H. Pasten}, Can. Math. Bull. 65, No. 4, 906--923 (2022; Zbl 1523.11134) Full Text: DOI arXiv
Jiang, Yujiao; Lü, Guangshi; Wang, Zhiwei Averaged forms of two conjectures of Erdős and Pomerance, and their applications. (English) Zbl 1506.11125 Adv. Math. 409, Part A, Article ID 108592, 42 p. (2022). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N37 11P55 11N25 11N36 PDFBibTeX XMLCite \textit{Y. Jiang} et al., Adv. Math. 409, Part A, Article ID 108592, 42 p. (2022; Zbl 1506.11125) Full Text: DOI
Chan, Stephanie Integral points on the congruent number curve. (English) Zbl 1510.11091 Trans. Am. Math. Soc. 375, No. 9, 6675-6700 (2022). Reviewer: Michel Waldschmidt (Paris) MSC: 11D45 11G05 11D25 PDFBibTeX XMLCite \textit{S. Chan}, Trans. Am. Math. Soc. 375, No. 9, 6675--6700 (2022; Zbl 1510.11091) Full Text: DOI arXiv
Mochizuki, Shinichi; Fesenko, Ivan; Hoshi, Yuichiro; Minamide, Arata; Porowski, Wojciech Explicit estimates in inter-universal Teichmüller theory. (English) Zbl 07564713 Kodai Math. J. 45, No. 2, 175-236 (2022). MSC: 14H25 14H30 PDFBibTeX XMLCite \textit{S. Mochizuki} et al., Kodai Math. J. 45, No. 2, 175--236 (2022; Zbl 07564713) Full Text: DOI Link
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
Győry, Kálmán \(S\)-unit equations and Masser’s ABC conjecture in algebraic number fields. (English) Zbl 1513.11103 Publ. Math. Debr. 100, No. 3-4, 499-511 (2022). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11D57 11D61 PDFBibTeX XMLCite \textit{K. Győry}, Publ. Math. Debr. 100, No. 3--4, 499--511 (2022; Zbl 1513.11103) Full Text: DOI
Dixit, Anup B.; Kim, Seoyoung; Murty, M. Ram Generalized Diophantine \(m\)-tuples. (English) Zbl 1489.11050 Proc. Am. Math. Soc. 150, No. 4, 1455-1465 (2022). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 11D45 11D72 11N36 PDFBibTeX XMLCite \textit{A. B. Dixit} et al., Proc. Am. Math. Soc. 150, No. 4, 1455--1465 (2022; Zbl 1489.11050) Full Text: DOI
Rittberg, Colin Jakob Intellectual humility in mathematics. (English) Zbl 07797743 Synthese 199, No. 3-4, 5571-5601 (2021). MSC: 00A30 00A35 PDFBibTeX XMLCite \textit{C. J. Rittberg}, Synthese 199, No. 3--4, 5571--5601 (2021; Zbl 07797743) Full Text: DOI
Táfula, Christian On Landau-Siegel zeros and heights of singular moduli. (English) Zbl 1483.11183 Acta Arith. 201, No. 1, 1-28 (2021). MSC: 11M20 11G50 11N37 PDFBibTeX XMLCite \textit{C. Táfula}, Acta Arith. 201, No. 1, 1--28 (2021; Zbl 1483.11183) Full Text: DOI arXiv Backlinks: MO
Louboutin, Stéphane R. On Ennola’s conjecture on non-Galois cubic number fields with exceptional units. (English) Zbl 1480.11138 Mosc. Math. J. 21, No. 4, 789-805 (2021). Reviewer: Balasubramanian Sury (Bangalore) MSC: 11R16 11R27 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Mosc. Math. J. 21, No. 4, 789--805 (2021; Zbl 1480.11138) Full Text: Link
König, Joachim; Legrand, François Density results for specialization sets of Galois covers. (English) Zbl 1481.11110 J. Inst. Math. Jussieu 20, No. 5, 1455-1496 (2021). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11R32 11G30 14E20 14G05 PDFBibTeX XMLCite \textit{J. König} and \textit{F. Legrand}, J. Inst. Math. Jussieu 20, No. 5, 1455--1496 (2021; Zbl 1481.11110) Full Text: DOI arXiv
Looper, Nicole R. Dynamical uniform boundedness and the \(abc\)-conjecture. (English) Zbl 1468.14059 Invent. Math. 225, No. 1, 1-44 (2021). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 14H25 37C25 11C08 11R09 14E05 37F10 11D41 PDFBibTeX XMLCite \textit{N. R. Looper}, Invent. Math. 225, No. 1, 1--44 (2021; Zbl 1468.14059) Full Text: DOI arXiv
Wada, Yuki Near miss \(abc\)-triples in compactly bounded subsets. (English) Zbl 1468.11129 RIMS Kôkyûroku Bessatsu B84, 193-227 (2021). MSC: 11G05 11D75 PDFBibTeX XMLCite \textit{Y. Wada}, RIMS Kôkyûroku Bessatsu B84, 193--227 (2021; Zbl 1468.11129) Full Text: Link
Grantham, Jon; Graves, Hester The abc conjecture implies that only finitely many \(s\)-Cullen numbers are repunits. (English) Zbl 1471.11125 J. Integer Seq. 24, No. 5, Article 21.5.3, 6 p. (2021). MSC: 11D61 11A63 11B83 PDFBibTeX XMLCite \textit{J. Grantham} and \textit{H. Graves}, J. Integer Seq. 24, No. 5, Article 21.5.3, 6 p. (2021; Zbl 1471.11125) Full Text: arXiv Link
Mochizuki, Shinichi Inter-universal Teichmüller theory. IV: Log-volume computations and set-theoretic foundations. (English) Zbl 1465.14005 Publ. Res. Inst. Math. Sci. 57, No. 1-2, 627-723 (2021). Reviewer: Peter Scholze (Bonn) MSC: 14-02 14H25 14H30 14G40 11Gxx PDFBibTeX XMLCite \textit{S. Mochizuki}, Publ. Res. Inst. Math. Sci. 57, No. 1--2, 627--723 (2021; Zbl 1465.14005) Full Text: DOI Backlinks: MO
van Frankenhuijsen, Machiel Two restricted ABC conjectures. (English) Zbl 1469.11240 J. Number Theory 221, 424-446 (2021). Reviewer: Michel Waldschmidt (Paris) MSC: 11J97 11D04 11D75 14G05 14G40 PDFBibTeX XMLCite \textit{M. van Frankenhuijsen}, J. Number Theory 221, 424--446 (2021; Zbl 1469.11240) Full Text: DOI arXiv
Pollack, Paul Multiplicative partitions of numbers with a large squarefree divisor. (English) Zbl 1486.11120 Ramanujan J. 53, No. 3, 595-605 (2020). Reviewer: Kaisa Matomäki (Turku) MSC: 11N56 11A51 11N32 11N64 PDFBibTeX XMLCite \textit{P. Pollack}, Ramanujan J. 53, No. 3, 595--605 (2020; Zbl 1486.11120) Full Text: DOI
Wang, Yi; Ding, Yuchen A note on balancing non-Wieferich primes. (English) Zbl 1463.11016 J. Anhui Norm. Univ., Nat. Sci. 43, No. 2, 129-133 (2020). MSC: 11A41 PDFBibTeX XMLCite \textit{Y. Wang} and \textit{Y. Ding}, J. Anhui Norm. Univ., Nat. Sci. 43, No. 2, 129--133 (2020; Zbl 1463.11016) Full Text: DOI
Laishram, Shanta; Luca, Florian; Sias, Mark On members of Lucas sequences which are products of factorials. (English) Zbl 1478.11018 Monatsh. Math. 193, No. 2, 329-359 (2020). MSC: 11B39 11B65 11D72 11D45 PDFBibTeX XMLCite \textit{S. Laishram} et al., Monatsh. Math. 193, No. 2, 329--359 (2020; Zbl 1478.11018) Full Text: DOI arXiv
Looper, Nicole R. The \(ABC\)-conjecture implies uniform bounds on dynamical Zsigmondy sets. (English) Zbl 1458.11107 Trans. Am. Math. Soc. 373, No. 7, 4627-4647 (2020). Reviewer: Riccardo Pengo (Lyon) MSC: 11G50 11R32 37P15 14G05 37P45 PDFBibTeX XMLCite \textit{N. R. Looper}, Trans. Am. Math. Soc. 373, No. 7, 4627--4647 (2020; Zbl 1458.11107) Full Text: DOI arXiv
Maire, Christian; Rougnant, Marine A note on \(p\)-rational fields and the abc-conjecture. (English) Zbl 1475.11209 Proc. Am. Math. Soc. 148, No. 8, 3263-3271 (2020). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R23 PDFBibTeX XMLCite \textit{C. Maire} and \textit{M. Rougnant}, Proc. Am. Math. Soc. 148, No. 8, 3263--3271 (2020; Zbl 1475.11209) Full Text: DOI arXiv
Chan, Tsz Ho Gaps between divisible terms in \(a^2(a^2 + 1)\). (English) Zbl 1468.11196 Bull. Aust. Math. Soc. 101, No. 3, 396-400 (2020); correction ibid. 103, No. 1, 176 (2021). MSC: 11N32 11A05 11B05 11B83 11G30 PDFBibTeX XMLCite \textit{T. H. Chan}, Bull. Aust. Math. Soc. 101, No. 3, 396--400 (2020; Zbl 1468.11196) Full Text: DOI arXiv
Peng, Wayne ABC implies there are infinitely many non-Fibonacci-Wieferich primes. (English) Zbl 1442.11056 J. Number Theory 212, 354-375 (2020). Reviewer: Krassimir Atanassov (Sofia) MSC: 11D41 11A41 11B39 PDFBibTeX XMLCite \textit{W. Peng}, J. Number Theory 212, 354--375 (2020; Zbl 1442.11056) Full Text: DOI
Jones, Lenny Monogenic polynomials with non-squarefree discriminant. (English) Zbl 1436.11125 Proc. Am. Math. Soc. 148, No. 4, 1527-1533 (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R04 11C08 11R09 PDFBibTeX XMLCite \textit{L. Jones}, Proc. Am. Math. Soc. 148, No. 4, 1527--1533 (2020; Zbl 1436.11125) Full Text: DOI
Hamahata, Yoshinori Arithmetic functions and the Cauchy product. (English) Zbl 1461.11012 Arch. Math. 114, No. 1, 41-50 (2020). MSC: 11A25 13F15 11D41 PDFBibTeX XMLCite \textit{Y. Hamahata}, Arch. Math. 114, No. 1, 41--50 (2020; Zbl 1461.11012) Full Text: DOI
Juul, Jamie; Krieger, Holly; Looper, Nicole; Manes, Michelle; Thompson, Bianca; Walton, Laura Arboreal representations for rational maps with few critical points. (English) Zbl 1436.11135 Balakrishnan, Jennifer S. (ed.) et al., Research directions in number theory. Women in numbers IV. Proceedings of the women in numbers, WIN4 workshop. Banff International Research Station, Banff, Alberta, Canada, August 14–18, 2017. Cham: Springer. Assoc. Women Math. Ser. 19, 133-151 (2019). MSC: 11R32 37P05 11F80 37P25 11R45 PDFBibTeX XMLCite \textit{J. Juul} et al., Assoc. Women Math. Ser. 19, 133--151 (2019; Zbl 1436.11135) Full Text: DOI arXiv
Bridy, Andrew; Oliver, Robert J. Lemke; Shallit, Arlo; Shallit, Jeffrey The generalized Nagell-Ljunggren problem: powers with repetitive representations. (English) Zbl 1475.11050 Exp. Math. 28, No. 4, 428-439 (2019). Reviewer: Michael A. Bennett (Vancouver) MSC: 11D61 11A63 11Y50 11D41 PDFBibTeX XMLCite \textit{A. Bridy} et al., Exp. Math. 28, No. 4, 428--439 (2019; Zbl 1475.11050) Full Text: DOI arXiv
Ding, Yuchen Non-Wieferich primes under the \(abc\) conjecture. (La conjecture \(abc\) et les nombres premiers qui ne satisfont pas la condition de Wieferich.) (English. French summary) Zbl 1435.11013 C. R., Math., Acad. Sci. Paris 357, No. 6, 483-486 (2019). MSC: 11A41 11N13 PDFBibTeX XMLCite \textit{Y. Ding}, C. R., Math., Acad. Sci. Paris 357, No. 6, 483--486 (2019; Zbl 1435.11013) Full Text: DOI
Chim, Kwok Chi; Shorey, Tarlok Nath; Sinha, Sneh Bala On Baker’s explicit \(abc\)-conjecture. (English) Zbl 1438.11091 Publ. Math. Debr. 94, No. 3-4, 435-453 (2019). Reviewer: Günter Lettl (Graz) MSC: 11D75 11J25 PDFBibTeX XMLCite \textit{K. C. Chim} et al., Publ. Math. Debr. 94, No. 3--4, 435--453 (2019; Zbl 1438.11091) Full Text: DOI
Rout, Sudhansu Sekhar Lucas non-Wieferich primes in arithmetic progressions. (English) Zbl 1415.11018 Funct. Approximatio, Comment. Math. 60, No. 2, 167-175 (2019). Reviewer: Lajos Hajdu (Debrecen) MSC: 11A41 11N13 PDFBibTeX XMLCite \textit{S. S. Rout}, Funct. Approximatio, Comment. Math. 60, No. 2, 167--175 (2019; Zbl 1415.11018) Full Text: DOI Euclid
Dutta, Utkal Keshari; Patel, Bijan Kumar; Ray, Prasanta Kumar Balancing non-Wieferich primes in arithmetic progressions. (English) Zbl 1428.11050 Proc. Indian Acad. Sci., Math. Sci. 129, No. 2, Paper No. 21, 7 p. (2019). MSC: 11B83 11B25 11A41 PDFBibTeX XMLCite \textit{U. K. Dutta} et al., Proc. Indian Acad. Sci., Math. Sci. 129, No. 2, Paper No. 21, 7 p. (2019; Zbl 1428.11050) Full Text: DOI
Chim, Kwok Chi; Nair, Saranya G.; Shorey, T. N. Explicit \(abc\)-conjecture and its applications. (English) Zbl 1440.11123 Hardy-Ramanujan J. 41, 143-156 (2018). MSC: 11J25 11D75 11N13 11A41 11D41 11Z05 PDFBibTeX XMLCite \textit{K. C. Chim} et al., Hardy-Ramanujan J. 41, 143--156 (2018; Zbl 1440.11123) Full Text: Link
da Silva, Natalia; Raianu, Serban; Salgado, Hector Differences of harmonic numbers and the \(abc\)-conjecture. (English) Zbl 1439.11009 PUMP J. Undergrad. Res. 1, 1-13 (2018). MSC: 11A07 11A41 11D45 PDFBibTeX XMLCite \textit{N. da Silva} et al., PUMP J. Undergrad. Res. 1, 1--13 (2018; Zbl 1439.11009) Full Text: arXiv Link
Nair, Saranya G.; Shorey, Tarlok N. On products from blocks of consecutive odd integers. (English) Zbl 1424.11087 Publ. Math. Debr. 92, No. 1-2, 1-15 (2018). Reviewer: László Tóth (Pécs) MSC: 11D72 11A41 11D45 PDFBibTeX XMLCite \textit{S. G. Nair} and \textit{T. N. Shorey}, Publ. Math. Debr. 92, No. 1--2, 1--15 (2018; Zbl 1424.11087) Full Text: DOI
Dubickas, Artūras; Sha, Min Multiplicative dependence of the translations of algebraic numbers. (English) Zbl 1423.11166 Rev. Mat. Iberoam. 34, No. 4, 1789-1808 (2018). Reviewer: Eira J. Scourfield (Egham) MSC: 11N25 11R04 11D61 PDFBibTeX XMLCite \textit{A. Dubickas} and \textit{M. Sha}, Rev. Mat. Iberoam. 34, No. 4, 1789--1808 (2018; Zbl 1423.11166) Full Text: DOI arXiv
Chen, Yong-Gao; Ding, Yu Corrigendum to “Non-Wieferich primes in arithmetic progressions”. (English) Zbl 1398.11020 Proc. Am. Math. Soc. 146, No. 12, 5485 (2018). MSC: 11A41 11B25 PDFBibTeX XMLCite \textit{Y.-G. Chen} and \textit{Y. Ding}, Proc. Am. Math. Soc. 146, No. 12, 5485 (2018; Zbl 1398.11020) Full Text: DOI
Clark, Pete L.; Watson, Lori D. ABC and the Hasse principle for quadratic twists of hyperelliptic curves. (ABC et le principe de Hasse pour les tordues de courbes hyperelliptiques.) (English. French summary) Zbl 1404.11091 C. R., Math., Acad. Sci. Paris 356, No. 9, 911-915 (2018). Reviewer: Rubén A. Hidalgo (Temuco) MSC: 11G30 14G05 PDFBibTeX XMLCite \textit{P. L. Clark} and \textit{L. D. Watson}, C. R., Math., Acad. Sci. Paris 356, No. 9, 911--915 (2018; Zbl 1404.11091) Full Text: DOI
Kotyada, Srinivas; Muthukrishnan, Subramani Non-Wieferich primes in number fields and \(abc\)-conjecture. (English) Zbl 1459.11016 Czech. Math. J. 68, No. 2, 445-453 (2018). Reviewer: Alessandro Cobbe (Neubiberg) MSC: 11R04 11A41 11R06 PDFBibTeX XMLCite \textit{S. Kotyada} and \textit{S. Muthukrishnan}, Czech. Math. J. 68, No. 2, 445--453 (2018; Zbl 1459.11016) Full Text: DOI arXiv
He, Yang-Hui; Hu, Zhi; Probst, Malte; Read, James Yang-Mills theory and the ABC conjecture. (English) Zbl 1388.81328 Int. J. Mod. Phys. A 33, No. 13, Article ID 1850053, 44 p. (2018). MSC: 81T13 81T60 82B20 81T30 14M25 14D21 PDFBibTeX XMLCite \textit{Y.-H. He} et al., Int. J. Mod. Phys. A 33, No. 13, Article ID 1850053, 44 p. (2018; Zbl 1388.81328) Full Text: DOI arXiv
Yasufuku, Yu Vojta’s conjecture on rational surfaces and the \(abc\) conjecture. (English) Zbl 1452.11090 Forum Math. 30, No. 3, 631-649 (2018). Reviewer: Michel Waldschmidt (Paris) MSC: 11J97 32H30 14G25 11B57 11J87 14G40 14J26 PDFBibTeX XMLCite \textit{Y. Yasufuku}, Forum Math. 30, No. 3, 631--649 (2018; Zbl 1452.11090) Full Text: DOI arXiv
Chan, Tsz Ho Common factors among pairs of consecutive integers. (English) Zbl 1429.11004 Int. J. Number Theory 14, No. 3, 871-880 (2018). MSC: 11A05 11B83 11D09 11G30 PDFBibTeX XMLCite \textit{T. H. Chan}, Int. J. Number Theory 14, No. 3, 871--880 (2018; Zbl 1429.11004) Full Text: DOI
Bridy, Andrew; Tucker, Thomas J. \(ABC\) implies a Zsigmondy principle for ramification. (English) Zbl 1407.37128 J. Number Theory 182, 296-310 (2018). Reviewer: David McKinnon (Waterloo) MSC: 37P05 11G50 14G25 PDFBibTeX XMLCite \textit{A. Bridy} and \textit{T. J. Tucker}, J. Number Theory 182, 296--310 (2018; Zbl 1407.37128) Full Text: DOI arXiv
Khan, Nadia; Katayama, Shin-ichi The abc conjecture and square free parts of Fibonacci numbers. (English) Zbl 1426.11008 J. Math., Tokushima Univ. 51, 5-28 (2017). MSC: 11B39 11D25 PDFBibTeX XMLCite \textit{N. Khan} and \textit{S.-i. Katayama}, J. Math., Tokushima Univ. 51, 5--28 (2017; Zbl 1426.11008)
Masser, D. W. Abcological anecdotes. (English) Zbl 1381.01010 Mathematika 63, No. 3, 713-714 (2017). MSC: 01A60 11-03 PDFBibTeX XMLCite \textit{D. W. Masser}, Mathematika 63, No. 3, 713--714 (2017; Zbl 1381.01010) Full Text: DOI
Aktaş, Kevser; Murty, M. Ram On the number of special numbers. (English) Zbl 1421.11074 Proc. Indian Acad. Sci., Math. Sci. 127, No. 3, 423-430 (2017). MSC: 11N25 11D59 PDFBibTeX XMLCite \textit{K. Aktaş} and \textit{M. R. Murty}, Proc. Indian Acad. Sci., Math. Sci. 127, No. 3, 423--430 (2017; Zbl 1421.11074) Full Text: DOI Backlinks: MO
Chen, Yong-Gao; Ding, Yu Non-Wieferich primes in arithmetic progressions. (English) Zbl 1422.11008 Proc. Am. Math. Soc. 145, No. 5, 1833-1836 (2017). MSC: 11A41 11N13 PDFBibTeX XMLCite \textit{Y.-G. Chen} and \textit{Y. Ding}, Proc. Am. Math. Soc. 145, No. 5, 1833--1836 (2017; Zbl 1422.11008) Full Text: DOI
Pasten, Hector Definability of Frobenius orbits and a result on rational distance sets. (English) Zbl 1419.11139 Monatsh. Math. 182, No. 1, 99-126 (2017). MSC: 11U05 11J97 52C10 PDFBibTeX XMLCite \textit{H. Pasten}, Monatsh. Math. 182, No. 1, 99--126 (2017; Zbl 1419.11139) Full Text: DOI
Aktaş, Kevser; Murty, M. Ram Fundamental units and consecutive squarefull numbers. (English) Zbl 1419.11006 Int. J. Number Theory 13, No. 1, 243-252 (2017). MSC: 11A25 11D09 PDFBibTeX XMLCite \textit{K. Aktaş} and \textit{M. R. Murty}, Int. J. Number Theory 13, No. 1, 243--252 (2017; Zbl 1419.11006) Full Text: DOI
Martin, Greg; Miao, Winnie \(abc\) triples. (English) Zbl 1406.11099 Funct. Approximatio, Comment. Math. 55, No. 2, 145-176 (2016). MSC: 11N32 11N25 11N05 11R29 PDFBibTeX XMLCite \textit{G. Martin} and \textit{W. Miao}, Funct. Approximatio, Comment. Math. 55, No. 2, 145--176 (2016; Zbl 1406.11099) Full Text: DOI arXiv Euclid Backlinks: MO
Rout, Sudhansu Sekhar Balancing non-Wieferich primes in arithmetic progression and \(abc\) conjecture. (English) Zbl 1419.11032 Proc. Japan Acad., Ser. A 92, No. 9, 112-116 (2016). MSC: 11B83 11B25 11A41 PDFBibTeX XMLCite \textit{S. S. Rout}, Proc. Japan Acad., Ser. A 92, No. 9, 112--116 (2016; Zbl 1419.11032) Full Text: DOI Euclid
Klurman, Oleksiy Radical of perfect numbers and perfect numbers among polynomial values. (English) Zbl 1346.11049 Int. J. Number Theory 12, No. 3, 585-591 (2016). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N25 11A25 PDFBibTeX XMLCite \textit{O. Klurman}, Int. J. Number Theory 12, No. 3, 585--591 (2016; Zbl 1346.11049) Full Text: DOI
Laishram, Shanta Baker’s explicit \(abc\)-conjecture and Waring’s problem. (English) Zbl 1408.11017 Hardy-Ramanujan J. 38, 49-52 (2016). MSC: 11D41 11D75 11E76 11P05 PDFBibTeX XMLCite \textit{S. Laishram}, Hardy-Ramanujan J. 38, 49--52 (2016; Zbl 1408.11017) Full Text: Link
Nair, Saranya G.; Shorey, T. N. Lower bounds for the greatest prime factor of product of consecutive positive integers. (English) Zbl 1400.11016 J. Number Theory 159, 307-328 (2016). MSC: 11A41 11D45 11D72 PDFBibTeX XMLCite \textit{S. G. Nair} and \textit{T. N. Shorey}, J. Number Theory 159, 307--328 (2016; Zbl 1400.11016) Full Text: DOI
Akbary, Amir; Yazdani, Soroosh On the greatest prime factor of some divisibility sequences. (English) Zbl 1394.11079 Cojocaru, A. C. (ed.) et al., SCHOLAR – a scientific celebration highlighting open lines of arithmetic research. Conference in honour of M. Ram Murty’s mathematical legacy on his 60th birthday, Centre de Recherches Mathématiques, Université de Montréal, Canada, October 15–17, 2013. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-1457-3/pbk; 978-1-4704-2843-3/ebook). Contemporary Mathematics 655. Centre de Recherches Mathématiques Proceedings, 1-13 (2015). MSC: 11T06 11G05 11J25 PDFBibTeX XMLCite \textit{A. Akbary} and \textit{S. Yazdani}, Contemp. Math. 655, 1--13 (2015; Zbl 1394.11079) Full Text: DOI arXiv
Tijdeman, Rob The \(abc\) conjecture. (Het \(abc\)-vermoeden.) (Dutch) Zbl 1344.11003 Nieuw Arch. Wiskd. (5) 16, No. 4, 234-237 (2015). MSC: 11-02 11-03 11D99 PDFBibTeX XMLCite \textit{R. Tijdeman}, Nieuw Arch. Wiskd. (5) 16, No. 4, 234--237 (2015; Zbl 1344.11003)
Halupczok, Karin Large sieve inequalities with general polynomial moduli. (English) Zbl 1322.11100 Q. J. Math. 66, No. 2, 529-545 (2015). Reviewer: Mehdi Hassani (Zanjan) MSC: 11N35 11N36 11N56 PDFBibTeX XMLCite \textit{K. Halupczok}, Q. J. Math. 66, No. 2, 529--545 (2015; Zbl 1322.11100) Full Text: DOI
Pasten, Hector The ABC conjecture, arithmetic progressions of primes and squarefree values of polynomials at prime arguments. (English) Zbl 1337.11065 Int. J. Number Theory 11, No. 3, 721-737 (2015). Reviewer: Paul Vojta (Berkeley) MSC: 11N32 11N13 11J97 11N36 PDFBibTeX XMLCite \textit{H. Pasten}, Int. J. Number Theory 11, No. 3, 721--737 (2015; Zbl 1337.11065) Full Text: DOI
Kane, Daniel M. On the number of ABC solutions with restricted radical sizes. (English) Zbl 1356.11017 J. Number Theory 154, 32-43 (2015). MSC: 11D85 11D45 11D75 PDFBibTeX XMLCite \textit{D. M. Kane}, J. Number Theory 154, 32--43 (2015; Zbl 1356.11017) 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 PDFBibTeX XMLCite \textit{T. Miyazaki}, Rocky Mt. J. Math. 45, No. 1, 303--344 (2015; Zbl 1378.11046) Full Text: DOI Euclid
Kühn, Ulf; Müller, Jan Steffen A height inequality for rational points on elliptic curves implied by the abc-conjecture. (English) Zbl 1395.11090 Funct. Approximatio, Comment. Math. 52, No. 1, 127-132 (2015). MSC: 11G05 11G50 PDFBibTeX XMLCite \textit{U. Kühn} and \textit{J. S. Müller}, Funct. Approximatio, Comment. Math. 52, No. 1, 127--132 (2015; Zbl 1395.11090) Full Text: DOI arXiv Euclid
Dietmann, Rainer; Marmon, Oscar Random Thue and Fermat equations. (English) Zbl 1364.11081 Acta Arith. 167, No. 2, 189-200 (2015). Reviewer: Günter Lettl (Graz) MSC: 11D41 11D45 11D59 PDFBibTeX XMLCite \textit{R. Dietmann} and \textit{O. Marmon}, Acta Arith. 167, No. 2, 189--200 (2015; Zbl 1364.11081) Full Text: DOI arXiv
Silva, Manuel; Freitas, Pedro J. The abc conjecture. (Portuguese) Zbl 1384.11062 Gaz. Mat., Lisb. 174, 41-42 (2014). MSC: 11D41 11-02 PDFBibTeX XMLCite \textit{M. Silva} and \textit{P. J. Freitas}, Gaz. Mat., Lisb. 174, 41--42 (2014; Zbl 1384.11062)
Mochizuki, Shinichi A panoramic overview of inter-universal Teichmüller theory. (English) Zbl 1403.14061 RIMS Kôkyûroku Bessatsu B51, 301-345 (2014). MSC: 14H25 14H30 PDFBibTeX XMLCite \textit{S. Mochizuki}, RIMS Kôkyûroku Bessatsu B51, 301--345 (2014; Zbl 1403.14061)
Etessami, Kousha; Stewart, Alistair; Yannakakis, Mihalis A note on the complexity of comparing succinctly represented integers, with an application to maximum probability parsing. (English) Zbl 1321.68309 ACM Trans. Comput. Theory 6, No. 2, Article No. 9, 23 p. (2014). MSC: 68Q25 11Y16 68Q42 PDFBibTeX XMLCite \textit{K. Etessami} et al., ACM Trans. Comput. Theory 6, No. 2, Article No. 9, 23 p. (2014; Zbl 1321.68309) Full Text: DOI arXiv
Sondow, Jonathan Lerch quotients, Lerch primes, Fermat-Wilson quotients, and the Wieferich-non-Wilson primes \(2, 3, 14771\). (English) Zbl 1371.11010 Nathanson, Melvyn B. (ed.), Combinatorial and additive number theory. Selected papers based on the presentations at the conferences CANT 2011 and 2012, New York, NY, USA, May 2011 and May 2012. New York, NY: Springer (ISBN 978-1-4939-1600-9/hbk; 978-1-4939-1601-6/ebook). Springer Proceedings in Mathematics & Statistics 101, 243-255 (2014). MSC: 11A41 11B68 PDFBibTeX XMLCite \textit{J. Sondow}, Springer Proc. Math. Stat. 101, 243--255 (2014; Zbl 1371.11010) Full Text: DOI arXiv
Gómez-Pérez, Domingo; Ostafe, Alina; Shparlinski, Igor E. On irreducible divisors of iterated polynomials. (English) Zbl 1339.11099 Rev. Mat. Iberoam. 30, No. 4, 1123-1134 (2014). MSC: 11T06 11L40 11T24 11P99 PDFBibTeX XMLCite \textit{D. Gómez-Pérez} et al., Rev. Mat. Iberoam. 30, No. 4, 1123--1134 (2014; Zbl 1339.11099) Full Text: DOI
Mihăilescu, Preda Around ABC. (English) Zbl 1384.11061 Eur. Math. Soc. Newsl. 93, 29-34 (2014). MSC: 11D41 11A41 PDFBibTeX XMLCite \textit{P. Mihăilescu}, Eur. Math. Soc. Newsl. 93, 29--34 (2014; Zbl 1384.11061) Full Text: Link
Robert, Olivier; Stewart, Cameron L.; Tenenbaum, Gérald A refinement of the \(abc\) conjecture. (English) Zbl 1357.11044 Bull. Lond. Math. Soc. 46, No. 6, 1156-1166 (2014). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D99 11N25 PDFBibTeX XMLCite \textit{O. Robert} et al., Bull. Lond. Math. Soc. 46, No. 6, 1156--1166 (2014; Zbl 1357.11044) Full Text: DOI
Piipponen, Samuli; Erkama, Timo Rational cycles of quadratic polynomials. (English) Zbl 1364.11145 JP J. Algebra Number Theory Appl. 33, No. 2, 113-132 (2014). MSC: 11R09 11R04 11D25 PDFBibTeX XMLCite \textit{S. Piipponen} and \textit{T. Erkama}, JP J. Algebra Number Theory Appl. 33, No. 2, 113--132 (2014; Zbl 1364.11145) Full Text: Link
Luca, F.; Saradha, N.; Shorey, T. N. Squares and factorials in products of factorials. (English) Zbl 1373.11029 Monatsh. Math. 175, No. 3, 385-400 (2014). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D45 11D72 11N36 PDFBibTeX XMLCite \textit{F. Luca} et al., Monatsh. Math. 175, No. 3, 385--400 (2014; Zbl 1373.11029) Full Text: DOI
Murty, M. Ram; Pasten, Hector Counting squarefree values of polynomials with error term. (English) Zbl 1318.11122 Int. J. Number Theory 10, No. 7, 1743-1760 (2014). Reviewer: Mihály Szalay (Budapest) MSC: 11N32 11C08 11G32 11J71 11K36 11K38 PDFBibTeX XMLCite \textit{M. R. Murty} and \textit{H. Pasten}, Int. J. Number Theory 10, No. 7, 1743--1760 (2014; Zbl 1318.11122) Full Text: DOI
von Känel, Rafael On Szpiro’s discriminant conjecture. (English) Zbl 1321.11070 Int. Math. Res. Not. 2014, No. 16, 4457-4491 (2014). Reviewer: Sungkon Chang (Savannah) MSC: 11G30 PDFBibTeX XMLCite \textit{R. von Känel}, Int. Math. Res. Not. 2014, No. 16, 4457--4491 (2014; Zbl 1321.11070) Full Text: DOI arXiv
de Weger, Benne A generalized Ramanujan-Nagell equation related to certain strongly regular graphs. (English) Zbl 1308.11041 Integers 14, Paper A35, 13 p. (2014). MSC: 11D61 11R29 11R11 11A51 05C10 PDFBibTeX XMLCite \textit{B. de Weger}, Integers 14, Paper A35, 13 p. (2014; Zbl 1308.11041) Full Text: EMIS
Bosser, Vincent; Surroca, Andrea Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture. (English) Zbl 1294.11113 Bull. Braz. Math. Soc. (N.S.) 45, No. 1, 1-23 (2014). Reviewer: Yu Yasufuku (Tokyo) MSC: 11G50 11G05 11J86 14G05 11G40 PDFBibTeX XMLCite \textit{V. Bosser} and \textit{A. Surroca}, Bull. Braz. Math. Soc. (N.S.) 45, No. 1, 1--23 (2014; Zbl 1294.11113) Full Text: DOI arXiv Link
Albis, Víctor S.; Villamizar, Nelly Y. The abc conjecture. (Spanish. English summary) Zbl 1381.11024 Lect. Mat. 34, No. 1, 11-75 (2013). MSC: 11D41 11D72 PDFBibTeX XMLCite \textit{V. S. Albis} and \textit{N. Y. Villamizar}, Lect. Mat. 34, No. 1, 11--75 (2013; Zbl 1381.11024)
Murty, M. Ram; Pasten, Hector Modular forms and effective Diophantine approximation. (English) Zbl 1297.11022 J. Number Theory 133, No. 11, 3739-3754 (2013). MSC: 11F11 11D75 11G05 PDFBibTeX XMLCite \textit{M. R. Murty} and \textit{H. Pasten}, J. Number Theory 133, No. 11, 3739--3754 (2013; Zbl 1297.11022) Full Text: DOI
Robert, Olivier; Tenenbaum, Gérald Asymptotic behaviour of the kernel of an integer. (Sur la répartition du noyau d’un entier.) (French. English summary) Zbl 1295.11103 Indag. Math., New Ser. 24, No. 4, 802-914 (2013). MSC: 11N25 PDFBibTeX XMLCite \textit{O. Robert} and \textit{G. Tenenbaum}, Indag. Math., New Ser. 24, No. 4, 802--914 (2013; Zbl 1295.11103) Full Text: DOI
Gratton, C.; Nguyen, K.; Tucker, T. J. \(ABC\) implies primitive prime divisors in arithmetic dynamics. (English) Zbl 1291.37121 Bull. Lond. Math. Soc. 45, No. 6, 1194-1208 (2013). Reviewer: Yu Yasufuku (Tokyo) MSC: 37P05 11G50 14G25 PDFBibTeX XMLCite \textit{C. Gratton} et al., Bull. Lond. Math. Soc. 45, No. 6, 1194--1208 (2013; Zbl 1291.37121) Full Text: DOI arXiv
Luca, Florian On the Diophantine equation \(f(n)=u!+v!\). (English) Zbl 1331.11024 Glas. Mat., III. Ser. 48, No. 1, 31-48 (2013). MSC: 11D85 PDFBibTeX XMLCite \textit{F. Luca}, Glas. Mat., III. Ser. 48, No. 1, 31--48 (2013; Zbl 1331.11024) Full Text: DOI
Drappeau, Sary On friable solutions of the equation \(a+b=c\). (Sur les solutions friables de l’équation \(a+b=c\).) (French. English summary) Zbl 1312.11020 Math. Proc. Camb. Philos. Soc. 154, No. 3, 439-463 (2013). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D45 11N25 11M06 PDFBibTeX XMLCite \textit{S. Drappeau}, Math. Proc. Camb. Philos. Soc. 154, No. 3, 439--463 (2013; Zbl 1312.11020) Full Text: DOI arXiv
Gawron, Maciej A note on the Diophantine equation \(P(z)=n!+m!\). (English) Zbl 1352.11036 Colloq. Math. 131, No. 1, 53-58 (2013). MSC: 11D85 11D04 PDFBibTeX XMLCite \textit{M. Gawron}, Colloq. Math. 131, No. 1, 53--58 (2013; Zbl 1352.11036) Full Text: DOI
Conrey, J. B.; Holmstrom, M. A.; McLaughlin, T. L. Smooth neighbors. (English) Zbl 1308.11104 Exp. Math. 22, No. 2, 195-202 (2013). Reviewer: Filip Najman (Zagreb) MSC: 11Y50 11N25 PDFBibTeX XMLCite \textit{J. B. Conrey} et al., Exp. Math. 22, No. 2, 195--202 (2013; Zbl 1308.11104) Full Text: DOI arXiv
Graves, Hester; Murty, M. Ram The abc conjecture and non-Wieferich primes in arithmetic progressions. (English) Zbl 1272.11014 J. Number Theory 133, No. 6, 1809-1813 (2013). Reviewer: Mohamed El Bachraoui (Al-Ain) MSC: 11A41 11N13 PDFBibTeX XMLCite \textit{H. Graves} and \textit{M. R. Murty}, J. Number Theory 133, No. 6, 1809--1813 (2013; Zbl 1272.11014) Full Text: DOI
Laishram, Shanta; Shorey, T. N. Baker’s explicit \(abc\)-conjecture and applications. (English) Zbl 1276.11048 Acta Arith. 155, No. 4, 419-429 (2012). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D41 11D45 11D61 PDFBibTeX XMLCite \textit{S. Laishram} and \textit{T. N. Shorey}, Acta Arith. 155, No. 4, 419--429 (2012; Zbl 1276.11048) Full Text: DOI arXiv
Murty, M. Ram; Murty, V. Kumar A variant of the Lang-Trotter conjecture. (English) Zbl 1276.11159 Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 461-474 (2012). MSC: 11N75 11F30 11G05 11R44 PDFBibTeX XMLCite \textit{M. R. Murty} and \textit{V. K. Murty}, in: Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer. 461--474 (2012; Zbl 1276.11159) Full Text: DOI
van Frankenhuijsen, Machiel About the ABC conjecture and an alternative. (English) Zbl 1267.11034 Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 169-180 (2012). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D75 11J86 PDFBibTeX XMLCite \textit{M. van Frankenhuijsen}, in: Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer. 169--180 (2012; Zbl 1267.11034) Full Text: DOI
Gusić, Ivica Some applications of the \(abc\)-conjecture to the Diophantine equation \(qy^{m}=f(x)\). (English) Zbl 1251.11018 Glas. Mat., III. Ser. 47, No. 1, 61-79 (2012). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D45 11D41 PDFBibTeX XMLCite \textit{I. Gusić}, Glas. Mat., III. Ser. 47, No. 1, 61--79 (2012; Zbl 1251.11018) Full Text: DOI
Lagarias, J. C.; Soundararajan, K. Counting smooth solutions to the equation \(A+B=C\). (English) Zbl 1270.11031 Proc. Lond. Math. Soc. (3) 104, No. 4, 770-798 (2012). Reviewer: Maurice Mignotte (Strasbourg) MSC: 11D45 11N25 11P55 PDFBibTeX XMLCite \textit{J. C. Lagarias} and \textit{K. Soundararajan}, Proc. Lond. Math. Soc. (3) 104, No. 4, 770--798 (2012; Zbl 1270.11031) Full Text: DOI arXiv
Zhang, Zhongfeng Powers in \(\prod_{k=1}^n (ak^{2^l\cdot3^m}+b)\). (English) Zbl 1309.11026 Funct. Approximatio, Comment. Math. 46, No. 1, 7-13 (2012). Reviewer: István Pink (Debrecen) MSC: 11D25 11D61 PDFBibTeX XMLCite \textit{Z. Zhang}, Funct. Approximatio, Comment. Math. 46, No. 1, 7--13 (2012; Zbl 1309.11026) Full Text: DOI Euclid
De Koninck, Jean-Marie; Luca, Florian Analytic number theory. Exploring the anatomy of integers. (English) Zbl 1247.11001 Graduate Studies in Mathematics 134. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7577-3/hbk). xviii, 414 p. (2012). Reviewer: Werner Kleinert (Berlin) MSC: 11-01 11A41 11B25 11N13 11N35 11N05 11A25 11K65 11N37 PDFBibTeX XMLCite \textit{J.-M. De Koninck} and \textit{F. Luca}, Analytic number theory. Exploring the anatomy of integers. Providence, RI: American Mathematical Society (AMS) (2012; Zbl 1247.11001)
Dąbrowski, Andrzej On the Brocard-Ramanujan problem and generalizations. (English) Zbl 1308.11039 Colloq. Math. 126, No. 1, 105-110 (2012). MSC: 11D61 11D99 PDFBibTeX XMLCite \textit{A. Dąbrowski}, Colloq. Math. 126, No. 1, 105--110 (2012; Zbl 1308.11039) Full Text: DOI
Saradha, N. Application of the explicit \(abc\)-conjecture to two Diophantine equations. (English) Zbl 1261.11036 Acta Arith. 151, No. 4, 401-419 (2012). Reviewer: Lajos Hajdu (Debrecen) MSC: 11D61 PDFBibTeX XMLCite \textit{N. Saradha}, Acta Arith. 151, No. 4, 401--419 (2012; Zbl 1261.11036) Full Text: DOI