Primes of the Form $p = x^2 + ny^2$

Speaker: Louis Arenas

Date: Thursday, August 6th

Time: 2:00pm

Abstract: In a letter to Mersenne, dated 1640, Fermat formulated a problem asking for sufficient conditions to the titular primes in the case when $n=1,2,3.$ The first well known proof to the original problem (in the case for when $n=1$) was published by Euler in 1749, with the other two cases being completed in 1772. Naturally, Euler attempted to generalize the problem for arbitrary integers n > 0; while not producing any proofs, the ideas that Euler touched on would be expanded by Legendre, Gauss, and Lagrange. The goal for this talk is to outline a strategy that answers Fermat’s original problem along with a few more cases. If time permits, we’ll just mention a result that solves the general problem for countably many n integers.

Link to Zoom meeting: https://zoom.us/j/98801740991

Video: Google Drive