Mathematical Colloquium

# Beyond Fermat's Last Theorem

By  David Zureick-Brown
From  Department of Mathematics
Emory University
When  Monday, February 12, 2018
4:00 pm
Where  Weber 223
Abstract

What do we (number theorists) do with ourselves now that Fermat's last theorem (FLT) has fallen? I'll discuss lots of generalizations of FLT (and some underlying intuitions) -- for instance, for integers a,b,c >= 2 satisfying 1/a + 1/b + 1/c < 1, Darmon and Granville proved the single generalized Fermat equation x^a + y^b = z^c has only finitely many coprime integer solutions; conjecturally something stronger is true: for a,b,c \geq 3 there are no non-trivial solutions and for (a,b,c) = (2,3,n) with n >= 10 the only solutions are the trivial solutions and (+- 3,-2,1) \$ (or (+-3,-2,+-1) \$ when n is even).

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