MathDB
{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

September 28, 2021
polynomialsum of digitsnumber theory

Problem Statement

Show that for every polynomial f(x)f(x) with integer coefficients, there exists a integer CC such that the set {n∈Z:\{n \in Z : the sum of digits of f(n)f(n) is C}C\} is not finite.