Yet another Proof of an old Hat

• Published in 2021
• Added on 2021-11-20

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

• http://arxiv.org/abs/2111.02788v1
• http://arxiv.org/pdf/2111.02788v1

Other information

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 = {2021-09-26},
	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}
}