2022 USAMO Problems/Problem 3

Problem

Let $\mathbb{R}_{>0}$ be the set of all positive real numbers. Find all functions $f:\mathbb{R}_{>0} \to \mathbb{R}_{>0}$ such that for all $x,y\in \mathbb{R}_{>0}$ we have $f(x) = f(f(f(x)) + y) + f(xf(y)) f(x+y).$

Solution

[WIP]

2022 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6
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2022 USAMO Problems/Problem 3

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