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?

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