Diophantine equations in separated variables and polynomial power sums

Abstract

We consider Diophantine equations of the shape $f(x)=g(y)$, where the polynomials $f$ and $g$ are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions $(x,y)$ with a bounded denominator are only possible in trivial cases.

arXiv comment6 pages