Resumen de Pillai’s Equation in Polynomials

Arturas Dubickas

• Let A, B, C be some nonconstant polynomials with coefficients in a field K of characteristic zero. We prove that the polynomial Pillai equation Ax−By=C has at most one solution in positive integers x, y except for three explicitly described triplets (A,B,C)∈K[t]3 when it has exactly two solutions in (x,y)∈N2.