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: 2

IMSC 2024, 5
Tags: imsc , polynomial , algebra
Let $\mathbb{R}_{>0}$ be the set of all positive real numbers. Find all strictly monotone (increasing or decreasing) functions $f:\mathbb{R}_{>0} \to \mathbb{R}$ such that there exists a two-variable polynomial $P(x, y)$ with real coefficients satisfying $$ f(xy)=P(f(x), f(y)) $$ for all $x, y\in\mathbb{R}_{>0}$.\\ [i]Proposed by Navid Safaei, Iran[/i]

IMSC 2024, 2
Tags: imsc , geometry
Let $ABC$ be an acute angled triangle and let $P, Q$ be points on $AB, AC$ respectively, such that $PQ$ is parallel to $BC$. Points $X, Y$ are given on line segments $BQ, CP$ respectively, such that $\angle AXP = \angle XCB$ and $\angle AYQ = \angle YBC$. Prove that $AX = AY$. [i]Proposed by Ervin Maci$\acute{c},$ Bosnia and Herzegovina[/i]