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f(x) is divisible by 3 for k, k+1, k+2. Prove for all x

Source:

October 4, 2010

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Problem Statement

(POL 3)

Given a polynomial

f(x)

with integer coefficients whose value is divisible by

3

for three integers

k, k + 1,

and

k + 2

. Prove that

f(m)

is divisible by

3

for all integers

m.