# Yet another Proof of an old Hat

- Published in 2021
- Added on

In the collections

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 of Fermat's Theorem expressing primes of the form \(1 + 4\mathbb{N}\) as sums of two squares.

## Links

### BibTeX entry

@article{YetanotherProofofanoldHat, title = {Yet another Proof of an old Hat}, author = {Roland Bacher}, url = {http://arxiv.org/abs/2111.02788v1 http://arxiv.org/pdf/2111.02788v1}, urldate = {2021-11-20}, year = 2021, 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 of Fermat's Theorem expressing primes of the form \(1 + 4\mathbb{\{}N{\}}\) as sums of two squares.}, comment = {}, archivePrefix = {arXiv}, eprint = {2111.02788}, primaryClass = {math.HO}, collections = {about-proof,attention-grabbing-titles,fun-maths-facts,integerology} }