On the Diophantine equation $pq=x^2+n{y}^2$

Ja Kyung Koo, Dong Hwa Shin

Let $n$ be a positive integer. We discuss pairs of distinct odd primes $p$ and $q$ not dividing $n$ for which the Diophantine equations $pq=x^2+n{y}^2$ have integer solutions in $x$…