Call \(a\) the "perfect square inverse" of \(b\) if \(a\) is the smallest possible integer such that \(ab\) is a perfect square. Is the following statement true or false?
"For each positive integer \(c\), there exists a positive integer \(d\) such that \(c\) is the perfect square inverse of \(d\)."
I think it is false. What do you think?