Mathematics
Sums of Squares and the Two-Square Theorem
Quick fact
A prime number p can be written as a sum of two squares if and only if p = 2 or p ≡ 1 (mod 4); no prime that is 3 mod 4 can ever be expressed that way.
Why this is interesting
You know that 25 = 16 + 9, so it's a sum of two squares. But why can't 6 be written that way? And is there a quick, foolproof way to tell which numbers can?