54

Part of 1969 IMO Shortlist

Problems(1)

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

Source:

(POL 3)

Given a polynomial

f(x)

with integer coefficients whose value is divisible by

3

for three integers

k, k + 1,

k + 2

f(m)

is divisible by

3

for all integers

m.

algebrapolynomialmodular arithmeticnumber theoryDivisibilityIMO ShortlistIMO Longlist