TY - JOUR
T1 - Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers
AU - Yekutieli, Amnon
N1 - Funding Information:
I wish to thank Eitan Bachmat, Moshe Newman, Noam Zimhoni, Moshe Kamenski, Ramin Takloo-Bighash, Gal Alster, Dor Amzaleg, Steven Miller, Hollis Williams, and Asaf Yekutieli for their advice in preparing this article. Thanks also to the anonymous referees, the editor of the journal, and its editorial board for their useful suggestions.
Publisher Copyright:
© 2023 The Author(s). Published with license by Taylor & Francis Group, LLC.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - 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 an enumeration of the normalized Pythagorean triples with a given hypotenuse. It also gives rise to an effective method for producing all such triples, and this effective method seems to be new. This paper is intended for the general mathematical audience, including undergraduate mathematics students. Therefore it contains background material, explanations, examples and drawings; and the proofs are complete.
AB - 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 an enumeration of the normalized Pythagorean triples with a given hypotenuse. It also gives rise to an effective method for producing all such triples, and this effective method seems to be new. This paper is intended for the general mathematical audience, including undergraduate mathematics students. Therefore it contains background material, explanations, examples and drawings; and the proofs are complete.
UR - http://www.scopus.com/inward/record.url?scp=85150519282&partnerID=8YFLogxK
U2 - 10.1080/00029890.2023.2176114
DO - 10.1080/00029890.2023.2176114
M3 - Article
AN - SCOPUS:85150519282
SN - 0002-9890
VL - 130
SP - 321
EP - 334
JO - American Mathematical Monthly
JF - American Mathematical Monthly
IS - 4
ER -