Question 62
Call admissible a set $A$ of integers that has the following property:
If $x, y \in A$ (possibly $x = y$) then $x^{2} + k x y + y^{2} \in A$ for every integer $k$.
Determine all pairs $m, n$ of nonzero integers such that the only admissible set containing both $m$ and $n$ is the set of all integers.
If $x, y \in A$ (possibly $x = y$) then $x^{2} + k x y + y^{2} \in A$ for every integer $k$.
Determine all pairs $m, n$ of nonzero integers such that the only admissible set containing both $m$ and $n$ is the set of all integers.