MathDB

5

Part of 2002 Austrian-Polish Competition

Problems(1)

Polynomial with integer coefficients

Source: 2002 Austrian-Polish, problem 5

9/23/2006
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.
algebrapolynomialmodular arithmeticalgebra unsolved