IMO Shortlist 2005 problem N7


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2. travnja 2012.
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Let P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots+a_{0}, where a_{0},\ldots,a_{n} are integers, a_{n}>0, n\geq 2. Prove that there exists a positive integer m such that P(m!) is a composite number.
Izvor: Međunarodna matematička olimpijada, shortlist 2005