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Polynomial with integer coefficients

Source: 2002 Austrian-Polish, problem 5

September 23, 2006
algebrapolynomialmodular arithmeticalgebra unsolved

Problem Statement

Let AA be the set {2,7,11,13}\{2,7,11,13\}. A polynomial ff with integer coefficients possesses the following property: for each integer nn there exists p∈Ap \in A such that p∣f(n)p|f(n). Prove that there exists p∈Ap \in A such that p∣f(n)p|f(n) for all integers nn.
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