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2018 USAMO Problems/Problem 2

Revision as of 03:15, 4 March 2023 by Wzs26843545602 (talk | contribs) (My solution of this problem a year or so ago is completely wrong, as is the one below it. f(x)=1/(1+x) works, for instance.)

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 $xyz =1.$


Solution

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