Description
Online Number Theory Seminar
Abstract: This talk is a continuation of the one given by István Pink (University of Debrecen) on March 18, 2022. The topic is the best possible general estimate of the number of solutions to a special type of the unit equations in two unknowns over the rationals. R. Scott and R. Styer conjectured in 2016 that for any fixed relatively prime positive integers $a, b$ and $c$ greater than 1 the equation $a^x + b^y = c^z$ has at most one solution in positive integers $x, y$ and $z,$ except for specific cases. In this talk we give a brief introduction to the conjecture, and present our results with their proofs, which in particular provides an analytic proof of the celebrated theorem of Scott (1993) solving the conjecture for $c = 2$ in a purely algebraic manner. This is a joint work with István Pink.
For access please contact the organizers (ntrg[at]science.unideb.hu).