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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.

Keywords

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}
}