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Possible Duplicate:
Triangular Factorials

Extending this question, what are the solutions $(m,n)$ of this equation?

$\sum_{k=1}^m{k} = n!$

I know $(1,1)$, $(3,3)$, and $(15,5)$. Are there any more? How can I prove the solution set is finite?

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    The abstract of [this paper](http://www.ams.org/journals/tran/2006-358-04/S0002-9947-05-03780-3/S0002-9947-05-03780-3.pdf) linked by [one of the answers](http://math.stackexchange.com/a/40968/1284) claims that there are only a finite number of solutions for some cases, but not including this one. This is definitely an exact duplicate but I don't think any of the answers to the other are satisfactory.2012-11-16

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