Pillai’s conjecture for polynomials

In this paper we study the polynomial version of Pillai’s conjecture on the exponential Diophantine equation (Formula presented) We prove that for any non-constant polynomial f there are only finitely many quadruples (n, m, deg p, deg q) consisting of integers n, m ≥ 2 and non-constant polynomials p, q such that Pillai’s equation holds. Moreover, we will give some examples that there can still be infinitely many possibil-ities for the polynomials p, q.