2019 USAMO Problems/Problem 1

Problem 1

Let $\mathbb{N}$ be the set of positive integers. A function $f:\mathbb{N}\to\mathbb{N}$ satisfies the equation $\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}$ for all positive integers $n$ . Given this information, determine all possible values of $f(1000)$ .

Solution

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

2019 USAMO (Problems • Resources)
First Problem	Followed by Problem 2
1 • 2 • 3 • 4 • 5 • 6
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2019 USAMO Problems/Problem 1

Problem 1

Solution

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