关于本原商高数的Terai猜想

On Terai'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,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.

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.