On Jeśmanowicz' conjecture concerning Pythagorean numbers
Let \(r,s\) be positive integers satisfying \(r>s\), \(2|r\) and \(\text{gcd} (r,s) =1\). The author proves that if \(2|r\), \(r\geq 81s\) and \(s\equiv 3\pmod 4\), then the equation \[ (r^2-s^2)^x +(2rs)^y =(r^2+s^2)^z \] has as the only solution \((x,y,z) =(2,2,2)\).
scientific article; zbMATH DE number 952365