Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers

• Published in 2021
• Added on 2021-02-12

It is well-known that pythagorean triples can be represented by points of the unit circle with rational coordinates. These points form an abelian group, and we describe its structure. This structural description yields, almost immediately, an enumeration of the normalized pythagorean triples with a given hypotenuse, and also to an effective method for producing all such triples. This effective method seems to be new. This paper is intended for the general mathematical audience, including undergraduate mathematics students, and therefore it contains plenty of background material, some history and several examples and exercises.

Links

• http://arxiv.org/abs/2101.12166v1
• http://arxiv.org/pdf/2101.12166v1

Other information

BibTeX entry

@article{PythagoreanTriplesComplexNumbersAbelianGroupsandPrimeNumbers,
	key = {PythagoreanTriplesComplexNumbersAbelianGroupsandPrimeNumbers},
	type = {article},
	title = {Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers},
	author = {Amnon Yekutieli},
	abstract = {It is well-known that pythagorean triples can be represented by points of the
unit circle with rational coordinates. These points form an abelian group, and
we describe its structure. This structural description yields, almost
immediately, an enumeration of the normalized pythagorean triples with a given
hypotenuse, and also to an effective method for producing all such triples.
This effective method seems to be new.
  This paper is intended for the general mathematical audience, including
undergraduate mathematics students, and therefore it contains plenty of
background material, some history and several examples and exercises.},
	comment = {},
	date_added = {2021-02-12},
	date_published = {2021-12-07},
	urls = {http://arxiv.org/abs/2101.12166v1,http://arxiv.org/pdf/2101.12166v1},
	collections = {fun-maths-facts,integerology,the-groups-group},
	url = {http://arxiv.org/abs/2101.12166v1 http://arxiv.org/pdf/2101.12166v1},
	year = 2021,
	urldate = {2021-02-12},
	archivePrefix = {arXiv},
	eprint = {2101.12166},
	primaryClass = {math.NT}
}