The Tarry -Escott Problem Over Quadratic Fields

Abstract

In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, 3, 4, 5 and 7, none of which can be directly derived from solutions over Z . We show that there are infinitely many solutions of the Tarry-Escott problem of degree 2 over an infinite family of rings Zn . We also solve some diophantine equations which have no integral solutions over some quadratic fields. We partially solve a generalized form of the Tarry-Escott problem of degree 2.