Talk:2008 IMO Problems/Problem 4
There are many interesting properties fo 
on can prove. The most interesting is probably
![\[f(xy) = f(x)f(y)\ \forall_{x,y \in \mathbb{R}^+}\]](http://latex.artofproblemsolving.com/a/f/3/af3252e23c66759fb0082bbad52f61d67f63f952.png)
So f must be an automorphism of the group 
.
If you assume (or can prove) that f must be continuous, then must be of the form 
for 
. (the only continuous automorphisms of the group)
Plugging this into the original functional equation gives 
.
I would like to see an alternative solution along these lines.
