1 Oct 2008; Mat-Nat Faculty (UiT), room A228. Wednesday 10:15-12:00

Marius Overholt

"Sums of two squares".

On Christmas Day 1640 Pierre de Fermat claimed in a letter to Marin Mersenne to have proved that every prime congruent to 1 modulo 4 can be written as a sum of two squares of integers. The first published proof of this theorem is due to Euler. In this talk I will give an overview of what is known about the integers that are sums of two squares, and discuss several open problems, some of which are known to be extremely difficult.