Elena C. Covill, Mohammad Javaheri, Nikolai A. Krylov
Published 2016-09-02Version 1
Equivalence classes of solutions of the Diophantine equation $a^2+mb^2=c^2$ form an infinitely generated abelian group $G_m$ under the operation induced by complex multiplication, where $m$ is a fixed square-free positive integer. Solutions of Pell's equation $x^2-my^2=1$ generate a subgroup $P_m$ of $G_m$. We prove that $G_m/P_m$ has infinite rank for infinitely many values of $m$. We also give several examples of $m$ for which $G_m/P_m$ has nontrivial torsion.
A basis of the group of primitive almost pythagorean triples
On the Diophantine equation cy^l=(x^p-1)/(x-1)
Solution of the Diophantine Equation $ x_{1}x_{2}x_{3}\cdots x_{m-1}=z^n $
![QR code for arXiv:1609.00440 [math.NT]](http://oss.arxitics.com/images/favicon.svg)