11.5

Part of 2005 All-Russian Olympiad Regional Round

Problems(1)

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

Source:

Prove that for any polynomial

P

with integer coefficients and any natural number

k

there exists a natural number

n

P(1) + P(2) + ...+ P(n)

is divisible by

k

number theoryInteger Polynomialpolynomialalgebra