A Quixotic Proof of Fermat's Two Squares Theorem for Prime Numbers
Number Theory
2022-10-17 v1
Abstract
Every odd prime number p can be written in exactly (p + 1)/2 ways as a sum ab+cd of two ordered products ab and cd such that min(a, b) > max(c, d). An easy corollary is a proof of Fermat's Theorem expressing primes in 1 + 4N as sums of two squares.
Cite
@article{arxiv.2210.07657,
title = {A Quixotic Proof of Fermat's Two Squares Theorem for Prime Numbers},
author = {Roland Bacher},
journal= {arXiv preprint arXiv:2210.07657},
year = {2022}
}