Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples II

JOURNAL OF NUMBER THEORY

卷:141

Article

Miyazaki, Takafumi¹  Yuan, Pingzhi²  Wu, Danyao² 

[1] Nihon Univ, Coll Sci & Technol, Dept Math, Chiyoda Ku, Tokyo 1018308, Japan

[2] S China Normal Univ, Sch Math, Guangzhou 510631, Guangdong, Peoples R China

关键词: Pythagorean triples;    Jesmanowicz' conjecture;    Exponential Diophantine equations;   

DOI  :  10.1016/j.jnt.2014.01.011

来源: Elsevier

【 摘 要 】

A conjecture proposed by Jesmanowicz on Pythagorean triples states that for any fixed primitive Pythagorean triple (a, b, c) such that a(2) + b(2) = c(2), the Diophantine equation a(x) + b(y) = c(z) has only the trivial solution in positive integers x, y and z. In this paper we establish the conjecture for the case where b is even and either a or c is congruent to +/- 1 modulo the product of all prime factors of b. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free