A Remark on Jesmanowicz' Conjecture for the Non-coprimality Case

作     者：Takafumi MIYAZAKI 

作者机构：Department of Mathematics College of Science and Technology Nihon University 1-8-14Kanda-SurugadaiChiyoda-kuTokyo 101-8308Japan 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2015年第31卷第8期

页      面：1255-1260页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by Grant in Aid for JSPS Fellows(Grant No.25484) 

主　　题：Diophantine equation Pythagorean numbers Jesmanowicz' conjecture 

摘      要：Let a, b, c be relatively prime positive integers such that a^2＋ b^2= c^2. Jesmanowicz＇conjecture on Pythagorean numbers states that for any positive integer N, the Diophantine equation（aN）x＋（b N）y=（cN）zhas no positive solution（x, y, z） other than x = y = z = 2. In this paper, we prove this conjecture for the case that a or b is a power of 2.