Sets of two equations with four variables, and their solutions – math.stackexchange.com
SirMrprofmol
Let $n$ be a natural number. Fix a system of two equations $S(n)$:
$$
\begin{cases} x^2+ny^2= z^2 \\ nx^2+y^2= t^2 \end{cases}
$$
where $x,y, z, t$ are positive integers. Next, $n \in M_1$ if that ...