Suppose there is a set of unequal natural numbers. The cardinality of the set is $n$.
For each number, $a_n$, in the set, ${a_n}^2$ is always nonzero multiples of $x$. ($x$ is nonzero integer.)
The product of all numbers in the set never becomes nonzero multiples of $x$.
How does one construct such set?
Also, if one replaces the constraint natural number/integer with some mathematical objects, while retaining "nonzero (integer) multiples of $x$", how does one construct such set?