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sum P(i) divisible by k All-Russian MO 2005 Regional 11.5

Source:

August 26, 2024
number theoryInteger Polynomialpolynomialalgebra

Problem Statement

Prove that for any polynomial PP with integer coefficients and any natural number kk there exists a natural number nn such that P(1)+P(2)+...+P(n)P(1) + P(2) + ...+ P(n) is divisible by kk.
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