2020 CAMO Problems/Problem 1

Revision as of 14:12, 5 September 2020 by Jbala (talk | contribs) (Created page with "==Problem 1== Let <math>f:\mathbb R_{>0}\to\mathbb R_{>0}</math> (meaning <math>f</math> takes positive real numbers to positive real numbers) be a nonconstant function such t...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $x$.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

2020 CAMO (ProblemsResources)
Preceded by
First problem
Followed by
Problem 2
1 2 3 4 5 6
All CAMO Problems and Solutions
2020 CJMO (ProblemsResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6
All CJMO Problems and Solutions

The problems on this page are copyrighted by the MAC's Christmas Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS