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Sad Number Theory

Source: 2019 USAMO 3, by Titu Andreescu, Cosmin Pohoata, and Vlad Matei

April 17, 2019
USAMOsaddersad stories2019 USAMO Problem 3Hisob

Problem Statement

Let KK be the set of all positive integers that do not contain the digit 77 in their base-1010 representation. Find all polynomials ff with nonnegative integer coefficients such that f(n)∈Kf(n)\in K whenever n∈Kn\in K.
Proposed by Titu Andreescu, Cosmin Pohoata, and Vlad Matei
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