Samuel Le Fourn (Université Grenoble Alpes): S-unit equation with powers

Online Number Theory Seminar

Abstract: In Runge's method and Baker's methods for integral points can be combined to improve the general bound on the solutions of the $S$-unit equation $ax + by = 1$ (with the best explicit bound obtained by Győry in 2019), which leads to several applications including explicit $abc$ bounds. In this talk, I will explain how the same ideas can be exploited for the $S$-unit equation $x^n + y = 1$ and how it could potentially be applied to the original $S$-unit equation.

For access please contact the organizers (ntrg[at]science.unideb.hu).