Which integers are sums of squares?
Prime numbers are the multiplicative atoms of the integers.
Every integer may be factored into a product of powers of distinct prime numbers in an essentially unique way.
There are many interesting questions concerning the behaviour of prime numbers with respect to the additive structure of the integers: for example, which primes are a sum of two squares? Is every integer a sum of four squares?
We found a solution to the latter question using projective geometry, and investigated generalisations of these problems using techniques from arithmetic geometry.
Benjamin Terence Moore