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2023 AMC 10BProblem 15P11-15~5 minPrint
Number PropertiesDivisibility & FactorsPrimesApply an identity: SFFT, sum of squares, difference of cubes, VietaUse an invariant, parity, or coloring argument

What is the least positive integer mm such that m⋅2!⋅3!⋅4!⋅5!…16!m \cdot 2! \cdot 3!\cdot 4!\cdot 5! \dots 16! is a perfect square?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.