Suppose that there is a set of natural numbers $a, b, c, d...$
Is there any such set that any product of two different numbers is a multiple of $x$, but any product of two same numbers - that is a number squared - is not a multiple of $x$?
How does one determine such set?
Edit: I want to know a general method for determining for any cardinality of a set. Not just two or so.