IMO 2016 Shortlist N1
For any positive integer k, denote the sum of digits of k in its decimal representation by S(k). Find all polynomials P(...
Category: Number Theory
Problem
For any positive integer k, denote the sum of digits of k in its decimal representation by S(k). Find all polynomials P(x) with integer coefficients such that for any positive integer n ⩾ 2016, the integer P(n) is positive and S(P(n)) = P(S(n)).