论一类特殊的Pythagoras数

A Special Class of Pythagoras Triplets

设x,y,z是正整数.如果x2+y2=z2,则称(x,y,z)是一组Pythagoras数.运用初等方法证明了:恰有12组Pythagoras数(x,y,z)适合6(x+y+z)=xy.

Let x, y z be positive integers. If x^2＋y^2=z^2, then （x, y, z） is called a Pythagoras triplet. In this paper, using some elementary methods, we prove that there exist exactly 12 Pythagoras triplets （x,y, z） satisfying 6（x＋ y＋ z）=xy.