关于本原商高数的Terai猜想

On Terae’s Conjecture Concerning Primitive Pythagorean Numbers

设(a,b,c)是一组适合a为偶数的本原商高数,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.

Let (a,b,c) be a primitive pythagorean triple with a is even. 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.