The Prouhet-Tarry-Escott problem, decomposability of polynomials and Diophantine equationsMPIM

by Lajos Hajdu (University of Debrecen)

Wednesday Feb 4, 2026, 2:30 PM → 3:30 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

The Prouhet-Tarry-Escott (PTE) problem asks to describe disjoint sets of integers for which there exists an integer k such that the associated first k power sum polynomials are equal. The problem has a vast literature, but unfortunately there is little known.

In the talk we describe a link between the PTE problem and decomposability of polynomials. Then we give applications for polynomial Diophantine equations, where at least one of the polynomials involved has only rational roots. The new results presented are joint with Á. Papp and R. Tijdeman.