Description
Online Number Theory Seminar
Abstract: By a theorem of Bilu and Tichy (2000) deep insight has been obtained into the structure of the rational solutions of the equation f(x) = g(y) for polynomials f,g with rational coefficients. Lajos Hajdu and I have worked out the consequences in case f has only simple rational roots, a case which occurs often in the literature. It turns out that Prouhet-Tarry-Escott pairs play an important role, in particular if both f and g have only simple rational roots. An ideal PTE-pair form two sets of n integers such that the monic polynomials with their elements as roots differ only by their constant term. We extended the notion to PTE-triples, -quadruples and -sextuples and studied the relation between PTE-sets and equations f(x) = g(y).
For access please contact the organizers (ntrg[at]science.unideb.hu).