Jeśmanowicz' conjecture for polynomials (Q2036614)

Let \(a,b,c\) be pairwise relatively prime integers such that \(a^2+b^2=c^2.\) It was conjectured by Jeśmanovicz in 1956 that the only positive integer solution of the equation \(a^x+b^y=c^z\) is \((x,y,z)=(2,2,2).\) The aim of the paper is to study an analogue of this conjecture for polynomials with coefficients in a field of characteristic zero.