I am a real newbie when it comes to funtions, and I don't understand what is supposed to happen or what I'm supposed to find when I get given an olympiad type question concerning functions. Could you help me out by solving, proving and explaining (it would be nice if you could) the following question? Thanks, any help is appreciated.
I think one of my teachers mentioned something about plugging in $m=0$ or something, but... Bleh, I don't know. Please help?
This question is taken from the South African Mathematics Olympiad of 1997.
Find all functions $f: \Bbb Z \to \Bbb Z $ which satisfy
$f(m+f(n)) = f(m) + n$
for all $m$, $n$ which are integers.
Thanks to everyone who helped me with this question :) I'm now one step further in my life...