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The group of
primitive almost pythagorean triples
Nikolai A. Krylov and Lindsay M. Kulzer
Vol. 6 (2013), No. 1, 13–24
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Abstract |
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We consider the triples of integer numbers that are solutions of the equation , where is a fixed, square-free arbitrary positive integer. The set of equivalence classes of these triples forms an abelian group under the operation coming from complex multiplication. We investigate the algebraic structure of this group and describe all generators for each . We also show that if the group has a generator with the third coordinate being a power of 2, such generator is unique up to multiplication by . |
Keywords
pythagorean triples, infinitely generated commutative
groups
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Mathematical Subject Classification 2010
Primary: 11D09, 20K20
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Milestones
Received: 11 August 2011
Revised: 29 March 2012
Accepted: 29 April 2012
Published: 23 June 2013
Communicated by Scott Chapman
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Authors |
| Nikolai A. Krylov | |
| Department of Mathematics Siena College 515 Loudon Road Loudonville, NY 12211 United States |
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| Lindsay M. Kulzer | |
| Department of Mathematics Siena College 515 Loudon Road Loudonville, NY 12211 United States |
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