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# Perfect square inverse

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?

Note by Shenal Kotuwewatta
2 years, 6 months ago