Talk:2008 IMO Problems/Problem 4
There are many interesting properties of one can prove. The most interesting could be
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.