Jeśmanowicz' conjecture and related equations

Jeśmanowicz conjectured that the exponential Diophantine equation (m^2-n^2)^x+(2mn)^y=(m^2+n^2)^zhas only the positive integer solution (x,y, z)=(2,2,2) where mand nare positive integers with m \gt n \gcd(m, n)=1and $m\not\equiv...