2

Part of Oliforum Contest III 2012

Problems(1)

{n \in Z: the sum of digits of f(n) is C} is not finite, integer polynomial f(x)

Source: Oliforum Contest III 2012 p2 https://artofproblemsolving.com/community/c2487525_oliforum_contest

Show that for every polynomial

f(x)

with integer coefficients, there exists a integer

C

such that the set

\{n \in Z :

the sum of digits of

f(n)

C\}

polynomialsum of digitsnumber theory