## Fermat’s Theorem on Sums of Two Squares

### Huixi Li – Clemson University

Fermatâ€™s theorem on sums of two squares states that an odd prime can be written as the sum of two integer squares if and only if it is congruent to 1 modulo 4. In this presentation I will talk about several proofs of this theorem, and I will compute the ratio of the sum of the bigger terms and the sum of the smaller terms in the representation of such primes as the sum of two squares of positive integers. The result verifies some conjectures of Zhiwei Sun.