Colorado State University   Mathematical

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

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).

Rachel Pries