IMO Shortlist 2016 problem N1


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3. listopada 2019.
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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 \geq 2016, the integer P(n) is positive and S(P(n)) = P(S(n)).

Izvor: https://www.imo-official.org/problems/IMO2016SL.pdf