Jeśmanowicz’ conjecture for polynomials

Let (a, b, c) be pairwise relatively prime integers such that $a^2 + b^2 = c^2 . In 1956, Jeśmanowicz conjectured that the only solution of a^x + b^y = c^z in positive integers is (x,y,z)=(2,2,2) . In this note we prove a polynomial analogue of this...