Question

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

Answer 1

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

Answer 2

Ishaaann heeelp me :(

Answer 3

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?

Answer 4

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

Answer 5

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

Answer 6

How can we come to that conclusion?

Answer 7

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

Answer 8

I don't follow the intuition. Probabilistic?

Answer 9

I can't think of any other function. :-/

Maybe @nikvist can solve it, he/she is good at math (and physics as well).

Answer 10

plz clarify \(f : \mathbb{N} \rightarrow ?\)

Answer 11

how about \(k\)....? real number? natural number?

Answer 12

@badreferences