The Group of Primitive Almost Pythagorean Triples

2011/07/14 by Nikolai A. Krylov, Krylov, Nikolai A., Lindsay M. Kulzer +1 · 1 citation
Mathematics · #11D09 #20K20 #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #math.GR #math.NT #msc:11D09 #msc:20K20

paper · pdf · doi:10.48550/arxiv.1107.2860

This is the version which will be published in Involve, a Journal of Mathematics. The reference list was extended and several remarks and comments reflecting the appearance of the new references were added to the main text

arxiv created 2012/05/09 · arxiv updated 2012/05/10

Abstract

We consider the triples of integer numbers that are solutions of the equation x²+qy²=z², where q 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 give a complete analysis when q∈\2,3,5,6\.

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