MathDB

7

Part of 2015 Korea Junior Math Olympiad

Problems(1)

Prove Schur's Theorem

Source: 2015 Korean Junior MO P7

11/1/2015
For a polynomial f(x)f(x) with integer coefficients and degree no less than 11, prove that there are infinitely many primes pp which satisfies the following.
There exists an integer nn such that f(n)≠0f(n) \not= 0 and ∣f(n)∣|f(n)| is a multiple of pp.
algebrapolynomial