关于商高数的Jemanowicz猜想

On Jesmanowicz' conjecture concerning Pythagorean numbers

设a,b是适合a>b,gcd(a,b)=1,2|ab的正整数,证明了当2||ab时,方程(a2-b2)x+ (2ab)y=(a2+b2)z仅有正整数解(x,y,z)=(2,2,2)可使x,y,z均为偶数。

Let a, b be positive integers such that a>b, gcd (a, b) - 1 and 2|ab, then it can be proved that if 2||ab, the equation (a2 - b2)x + (2ab)y = (a2 + b2)z has only the positive integer solution (x, y, z) = (2, 2, 2) with x=y=z=0(mod2).