This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2019 USAMO, 3
Let $K$ be the set of all positive integers that do not contain the digit $7$ in their base-$10$ representation. Find all polynomials $f$ with nonnegative integer coefficients such that $f(n)\in K$ whenever $n\in K$. [i]Proposed by Titu Andreescu, Cosmin Pohoata, and Vlad Matei[/i]
sob mathematical induction modular arithmetic number theory polynomials proof by contradiction