On perfect powers that are sums of cubes of a five term arithmetic progression

JOURNAL OF NUMBER THEORY

卷:201

Article

Argaez-Garcia, Alejandro^1,2 

[1] Univ Autonoma Yucatan, Fac Ingn Quim, Perifer Norte Kilometro 33-5, Merida 97200, Yucatan, Mexico

[2] Ctr Invetigac Matemat AC, Unidad Merida, Parque Cient & Tecnol Yucatan Km 5-5, Merida 97302, Yucatan, Mexico

关键词: Exponential equation;    Galois representation;    Frey-Hellegouarch curve;    Modularity;    Evel lowering;    Lehmer sequences;    Primitive divisors;   

DOI  :  10.1016/j.jnt.2019.02.014

来源: Elsevier

【 摘 要 】

We prove that the equation (x - 2r)(3) + (x - r)(3) + x(3) + (x + r)(3) + (x + 2r)(3) = y(P) only has solutions which satisfy xy = 0 for 1 <= r <= 10(6) and p >= 5 prime. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free