Yet another Proof of an old Hat

• Published in 2021
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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.

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},
}