Here is an interesting problem that I've been thinking about for a while: Let p be a prime s.t. p = 4m+1 for some integer m. Show that p divides n^2 + 1, where n = (2m)! It comes from a section on principal ideal domains and unique factorization domains. It is well-known that p is the sum of squares of two integers and thus is a norm of a Gaussian prime, and n^2 + 1 = (n+i)*(n-i). However, I am not sure that this helps anything. Does anyone have any ideas. Your help is greatly appreciated.