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

Tags were heavily modified to better represent problems.

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Found problems: 2

2019 USAMO, 3
Tags: USAMO , sadder , sad stories , 2019 USAMO Problem 3 , Hi , sob
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]

2019 USAMO, 6
Tags: USAMO , sad stories , sadder , 2019 USAMO Problem 6 , Polynomials , Weird problem , the saddest
Find all polynomials $P$ with real coefficients such that $$\frac{P(x)}{yz}+\frac{P(y)}{zx}+\frac{P(z)}{xy}=P(x-y)+P(y-z)+P(z-x)$$ holds for all nonzero real numbers $x,y,z$ satisfying $2xyz=x+y+z$. [i]Proposed by Titu Andreescu and Gabriel Dospinescu[/i]