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Are there any positive integer solutions $(n,x)$ to the equation $(x)(x+1)=n!$ except $(2,1)$ and $(3,2)$?

If not (as I suspect is the case), how do you prove that?

In general, is there a way to approach the Diophantine equation $n!=P(x)$ where $P$ is a polynomial?

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@Vincent Please stop suggesting trivial edits to old questions. Every time a question is edited, it gets bumped to the front page. You're flooding the front page with old questions, which is against recommendations for editing old questions. – apnorton Aug 27 '14 at 21:54
up vote 7 down vote accepted

This question was discussed on mathoverflow, and the question is open.

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