Pythagorean Triples, Complex Numbers, Abelian Groups and Prime Numbers

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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.

Original languageEnglish
Pages (from-to)321-334
Number of pages14
JournalAmerican Mathematical Monthly
Issue number4
StatePublished - 1 Jan 2023

ASJC Scopus subject areas

  • General Mathematics


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