Let , where are integers, , . Prove that there exists a positive integer such that is a composite number.
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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
Školjka 
, where 
are integers, 
, 
. Prove that there exists a positive integer 
such that 
is a composite number.