Question 17
Determine if there exists a (three-variable) polynomial $P(x, y, z)$ with integer coefficients satisfying the following property: A positive integer $n$ is *not* a perfect square if and only if there is a triple $(x, y, z)$ of positive integers such that $P(x, y, z) = n$.
(This problem was suggested by Gerhard Woeginger.)
(This problem was suggested by Gerhard Woeginger.)