Mike Bennett (University of British Columbia): Differences between perfect powers : The Lebesgue-Nagell equation

Online Number Theory Seminar

Abstract: I discuss what is provable with current technology about the classical Diophantine equation $x^2+D=y^n$, when the prime divisors of $D$ are restricted to a fixed finite set $S$. This is joint work with Samir Siksek and, in part, with Philippe Michaud-Jacobs. Our results rely upon a combination of various results based upon the modularity of Galois representations, with bounds for linear forms in logarithms.

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