Problem 137

We say that $N$ is powerful if whenever $p\mid N$ we also have $p^2\mid N$ . Let $k\geq 3$ . Can the product of any $k$ consecutive positive integers ever be powerful?

Source: erdosproblems.com/137

Number theory
Powerful numbers

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Open

No claim settles this problem.

Er82c: Erdős, P., Miscellaneous problems in number theory. Congr. Numer. (1982), 25-45.
Er97c: Erdős, Paul, Some of my favorite problems and results. The mathematics of Paul Erdős, I (1997), 47-67.
ErGr80: Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).
ErSe75: Erdős, P. and Selfridge, J. L., The product of consecutive integers is never a power. Illinois J. Math. (1975), 292-301.

Problem 137

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