Interesting Esoterica

Yet another Proof of an old Hat

Article by Roland Bacher
  • Published in 2021
  • Added on
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.

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Other information

key
YetanotherProofofanoldHat
type
article
date_added
2021-11-20
date_published
2021-01-22

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 = {2021-01-22},
	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}
}