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2018 USAMO Problems/Problem 2

Revision as of 10:51, 21 April 2018 by Sujaykazi (talk | contribs) (Created page with "==Problem 2== Find all functions <math>f:(0,\infty) \rightarrow (0,\infty)</math> such that <cmath>f\left(x+\frac{1}{y}\right)+f\left(y+\frac{1}{z}\right) + f\left(z+\frac{1}...")
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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 $xyz =1.$


Solution

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