# 2018 USAMO Problems/Problem 2

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## Problem 2

Find all functions $f:(0,\infty) \rightarrow (0,\infty)$ such that

$$f\left(x+\frac{1}{y}\right)+f\left(y+\frac{1}{z}\right) + f\left(z+\frac{1}{x}\right) = 1$$ for all $x,y,z >0$ with $xyz =1.$