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Factorial equation - Find all such m

Source: Mediterranean MO 2004

October 31, 2010
factorialinequalitiesnumber theoryprime factorizationnumber theory unsolved

Problem Statement

Find all natural numbers mm such that 1!⋅3!⋅5!⋯(2m−1)!=(m(m+1)2)!.1! \cdot 3! \cdot 5! \cdots (2m-1)! = \biggl( \frac{m(m+1)}{2}\biggr) !.
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