# 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

## Other information

- key
- YetanotherProofofanoldHat
- type
- article
- date_added
- 2021-11-20
- date_published
- 2021-07-11

### BibTeX entry

@article{YetanotherProofofanoldHat, key = {YetanotherProofofanoldHat}, type = {article}, title = {Yet another Proof of an old Hat}, author = {Roland Bacher}, 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 = {}, date_added = {2021-11-20}, date_published = {2021-07-11}, urls = {http://arxiv.org/abs/2111.02788v1,http://arxiv.org/pdf/2111.02788v1}, collections = {about-proof,attention-grabbing-titles,fun-maths-facts,integerology}, url = {http://arxiv.org/abs/2111.02788v1 http://arxiv.org/pdf/2111.02788v1}, urldate = {2021-11-20}, year = 2021, archivePrefix = {arXiv}, eprint = {2111.02788}, primaryClass = {math.HO} }