Generalizations of classical results on Jesmanowicz' conjecture concerning Pythagorean triples

JOURNAL OF NUMBER THEORY

卷:133

Article

Miyazaki, Takafumi

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

DOI  :  10.1016/j.jnt.2012.08.018

来源: Elsevier

【 摘 要 】

In 1956 L. Jesmanowicz conjectured, for any primitive Pythagorean triple (a, b, c) satisfying a(2) + b(2) = c(2), that the equation a(x) + b(y) = c(z) has the unique solution (x, y, z) = (2,2,2) in positive integers x, y and z. This is a famous unsolved problem on Pythagorean numbers. In this paper we broadly extend many of classical well-known results on the conjecture. As a corollary we can verify that the conjecture is true if a - b = +/- 1. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free