USAMO 2019 Problem 3

Day 1
Difficulty band 8

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 $n\in K$ .

Proposed by Titu Andreescu, Cosmin Pohoata, and Vlad Matei

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.

Add a solution

Locator usamo/2019/p3 · Tag XF8E33V559 · Edit this page on GitHub · Keys: j next, k previous