Find all equations that satisfy: {f(f(n))=n+k|n∈ℕ}.

Question

turingtest · Answer

oh man, I've been seeing this question and it's really not my forte
I just like watching people like Ishaan solve this ;)

anonymous · Answer

Ishaaann heeelp me :(

anonymous · Answer

Lol I don't think I can help much here. I don't know what the standard procedure is...

btw is f(x) = x + c, going to work?

anonymous · Answer

It's one of the equations, I think. I'm trying to determine others.

anonymous · Answer

Is the equation f(f(n))=n+k, enough to assume it's invertible?

anonymous · Answer

How can we come to that conclusion?

anonymous · Answer

Just an intuition, f(f(n)) is linear but it's not continuous

anonymous · Answer

I don't follow the intuition. Probabilistic?

anonymous · Answer

I can't think of any other function.  :-/

Maybe @nikvist can solve it, he/she is good at math (and physics as well).

anonymous · Answer

plz clarify  $f : \mathbb{N} \rightarrow ?$

anonymous · Answer

how about $k$....? real number? natural number?

anonymous · Answer

@badreferences