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arXiv · 1404.1060

On the Diophantine equation $pq=x^2+ny^2$

Ja Kyung Koo·Dong Hwa Shin
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Abstract

Let $n$ be a positive integer. We discuss pairs of distinct odd primes $p$ and $q$ not dividing $n$ for which the Diophantine equations $pq=x^2+ny^2$ have integer solutions in $x$ and $y$. As its examples we classify all such pairs of $p$ and $q$ when $n=5$ and $14$.

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Ja Kyung Koo, Dong Hwa Shin. 2014-04-17. On the Diophantine equation $pq=x^2+ny^2$. https://arxiv.org/abs/1404.1060

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