Volume no :16, Issue no: 2, December (2016)

Journal of Algebra, Number Theory: Advances and Applications

A BASIS OF THE GROUP OF PRIMITIVE ALMOST PYTHAGOREAN TRIPLES

Author's: Nikolai A. Krylov
Pages: [51] - [70]
Received Date: September 20, 2016
Submitted by:
DOI: http://dx.doi.org/10.18642/jantaa_7100121720

Abstract

Let m be a fixed square-free positive integer, then equivalence classes of solutions of Diophantine equation form an infinitely generated abelian group under the operation induced by the complex multiplication. A basis of this group is constructed here using prime ideals and the ideal class group of the field

Keywords

almost Pythagorean triples, prime ideals, imaginary quadratic field, ideal class group.