Yet another Proof of an old Hat
Roland Bacher (IF)

TL;DR
This paper presents a new proof of Fermat's theorem on sums of two squares for primes of the form 1+4N, based on a combinatorial property of odd primes expressed through sums of ordered products.
Contribution
It introduces a novel combinatorial approach to prove Fermat's theorem, providing an alternative perspective on sums of two squares for specific primes.
Findings
Every odd prime p can be expressed as a sum of two products in exactly (p+1)/2 ways.
The number of such representations relates directly to Fermat's theorem on sums of two squares.
The proof offers a new combinatorial insight into classical number theory results.
Abstract
Every odd prime number p can be written in exactly (p + 1)/2 ways as a sum ab + cd with min(a, b) > max(c, d) of two ordered products. This gives a new proof Fermat's Theorem expressing primes of the form 1 + 4N as sums of two squares 1 .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHistory and Theory of Mathematics · Mathematics and Applications · Advanced Mathematical Theories
