MathDB
P(m!) is composite

Source: IMO Shortlist 2005, N7

March 19, 2007
polynomialnumber theorycomposite numbersalgebraIMO Shortlist

Problem Statement

Let P(x)=anxn+an−1xn−1+…+a0P(x)=a_{n}x^{n}+a_{n-1}x^{n-1}+\ldots+a_{0}, where a0,…,ana_{0},\ldots,a_{n} are integers, an>0a_{n}>0, n≥2n\geq 2. Prove that there exists a positive integer mm such that P(m!)P(m!) is a composite number.
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