Diophantine equations in separated variables and polynomial power sums

Abstract

We consider Diophantine equations of the shape $f\left(x\right)=g\left(y\right)$ , 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.

Keywords: Bilu–Tichy theorem; Diophantine equation; Linear recurrences.