Question 91
A set $A$ of integers is called admissible if it has the following property: for all $x, y \in A$ (not necessarily distinct) and for every $k \in \mathbb{Z}$, we have $x^{2}+k x y+y^{2} \in A$.
Determine all pairs of nonzero integers $(m, n)$ such that the only admissible set containing both $m$ and $n$ is $\mathbb{Z}$.
Determine all pairs of nonzero integers $(m, n)$ such that the only admissible set containing both $m$ and $n$ is $\mathbb{Z}$.