Perfect powers in sum of three fifth powers

JOURNAL OF NUMBER THEORY

卷:236

Article

Das, Pranabesh¹  Dey, Pallab Kanti^2,3  Koutsianas, Angelos⁴  Tzanakis, Nikos⁵ 

[1] Univ Waterloo, Pure Math, 200 Univ Ave West, Waterloo, ON N2L 3G1, Canada

[2] Ramakrishna Mission Vivekananda Educ & Res Inst, Dept Math, Howrah 711202, W Bengal, India

[3] SRM Univ AP, Amaravati 522502, Andhra Pradesh, India

[4] Univ British Columbia, Dept Math, 1984 Math Rd, Vancouver, BC V6T 1Z2, Canada

[5] Univ Crete, Dept Math & Appl Math, Voutes Campus, Iraklion 70013, Greece

关键词: Diophantine equation;    Galois representation;    Frey curve;    Modularity;    Level lowering;    Sum of perfect powers;   

DOI  :  10.1016/j.jnt.2021.07.029

来源: Elsevier

【 摘 要 】

In this paper we determine the perfect powers that are sums of three fifth powers in an arithmetic progression. More precisely, we completely solve the Diophantine equation (x - d)5 + x5 + (x + d)5 = zn, n > 2, where d, x, z is an element of Z and d = 2a5b with a, b > 0. (c) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free