The Group of Primitive Almost Pythagorean Triples

Details The Group of Primitive Almost Pythagorean Triples The Group of Primitive Almost Pythagorean Triples

2011-07-14

arxiv.org/abs/1107.2860v1

Mathematics

Number Theory

Scientific paper

We consider the triples of integer numbers that are solutions of the equation
$x^2+qy^2=z^2$, 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 $q\in\{2,3,5,6\}$.

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