Let(a,b,c) be a primitive Pythagorean triple with a is even. In this paper we prove that if c is a prime power,then the equation x~2+b~y=c~z has only the positive integer solution(x,y,z)=(a,2,2) with y is even.

• 设(a；b；c)是一组适合a为偶数的本原商高数；该文证明了:当c是素数方幂时；方程x2+by=cz仅有正整数解(x；y；z)=(a；2；2)可使y是偶数.