A basis of the group of primitive almost pythagorean triples

Nikolai A. Krylov

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arXiv · 1401.2869

A basis of the group of primitive almost pythagorean triples

Nikolai A. Krylov

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Abstract

Let $m$ be a fixed square-free positive integer, then equivalence classes of solutions of Diophantine equation $x^2+m\cdot y^2=z^2$ 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 $\mathbb Q (\sqrt{-m})$.

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Nikolai A. Krylov. 2014-01-13. A basis of the group of primitive almost pythagorean triples. https://arxiv.org/abs/1401.2869

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