关于Jeśmanowicz关于原始毕达哥拉斯三元组猜想的一个开放问题

Pub Date : 2019-12-11 DOI:10.3336/gm.54.2.02

Hai Yang, Ruiqin Fu

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引用次数: 1

摘要

设m > 31为偶数，且gcd(m, 31) = 1。本文用一些初等方法证明了方程(m2−312)x +(62m) = (m2 +312)z只有正整数解(x, y, z) =(2,2,2)。这一结果解决了T. Miyazaki (Acta Arith. 186(2018)， 1-36)关于Jeśmanowicz关于原始毕达哥拉斯三组猜想的一个开放问题。

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An open problem on Jeśmanowicz' conjecture concerning primitive Pythagorean triples

Let m > 31 be an even integer with gcd(m, 31) = 1. In this paper, using some elementary methods, we prove that the equation (m2 −312)x +(62m) = (m2 +312)z has only the positive integer solution (x, y, z) = (2, 2, 2). This result resolves an open problem raised by T. Miyazaki (Acta Arith. 186 (2018), 1–36) about Jeśmanowicz’ conjecture concerning primitive Pythagorean triples.

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