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Prove Schur's Theorem

Source: 2015 Korean Junior MO P7

November 1, 2015

algebrapolynomial

Problem Statement

For a polynomial

f(x)

with integer coefficients and degree no less than

1

, prove that there are infinitely many primes

p

which satisfies the following.
There exists an integer

n

such that

f(n) \not= 0

and

|f(n)|

is a multiple of

p