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Part of 2012 Turkey MO (2nd round)

Problems(1)

Turkey NMO 2012 Problem 1

Source: Turkey NMO 2012

11/24/2012
Find all polynomials with integer coefficients such that for all positive integers nn satisfies P(n!)=∣P(n)∣!P(n!)=|P(n)|!
algebrapolynomialnumber theory proposednumber theory