# 2020 CAMO Problems/Problem 1

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## Problem 1

Let $f:\mathbb R_{>0}\to\mathbb R_{>0}$ (meaning $f$ takes positive real numbers to positive real numbers) be a nonconstant function such that for any positive real numbers $x$ and $y$, $$f(x)f(y)f(x+y)=f(x)+f(y)-f(x+y).$$Prove that there is a constant $a>1$ such that $$f(x)=\frac{a^x-1}{a^x+1}$$for all positive real numbers $x$.