论文标题
关于Erds和Straus的猜想的评论
A remark on a conjecture of Erdős and Straus
论文作者
论文摘要
本说明的目的是表明，鉴于积极的整数$ n \ geq 5 $，Diophantine方程的积极积分解决方案$ 4/n = 1/x + 1/y + 1/z $不能具有解决方案，因此$ x $ and $ y $是$ xy <\\ sqrt {z/2} $ $ xy <\ xy <\ sqrt {z/2} $。证明使用$ 4/n $的持续分数扩展。
The aim of this note is to show that given a positive integer $n \geq 5$, the positive integral solutions of the diophantine equation $4/n = 1/x + 1/y+1/z$ cannot have solution such that $x$ and $y$ are coprime with $xy < \sqrt{z/2}$. The proof uses the continued fraction expansion of $4/n$.
