LGRT 1681
Fermat's Last Theorem states that for any n greater than 2, there do not exist integer solutions to x^n + y^n = z^n where all of x, y, z are non-zero. This theorem intrigued and vexed mathematicians for over 350 years from when Fermat claimed he had a proof to when Wiles finally proved it using elliptic curves and modularity. Along the way, attempts to solve or partially solve the problem led to many developments in number theory. In this talk, we will discuss the history of the theorem, the developments in number theory it led to, and some partial proofs including the proofs of the n=4 case and Kummer's proof where n is a specific type of prime called "regular".