Je{ś}manowicz' conjecture for polynomials

Abstract

Let $(a,b,c)$ be pairwise relatively prime integers such that $a^2+b^2=c^2$. In 1956, Je{ś}manowicz 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 conjecture.

14 pages