Here is an interesting problem that I've been thinking about for a while:(adsbygoogle = window.adsbygoogle || []).push({});

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Pythagorean Primes and Gaussian Primes, divisibility question

**Physics Forums | Science Articles, Homework Help, Discussion**