Function Olympiad Problem: Define $f(n)$ such that $f(n)$ is a positive integer, $f(n+1)$ $>$ $f(n)$ and $f(f(n))$ $=$ $3n$. The value of $f(10)$ is?
44238
Let $f: \mathbb N \rightarrow \mathbb N$ are increasing function such that $f\left(f(n)\right)=3n$. Find $f(2017)$
25563
Count number of increasing functions, nondecreasing functions $f: \{1, 2, 3, \ldots, n\} \to \{1, 2, 3, \ldots, m\}$, with $m \geq n$.
50552
find functions that $f(m+k)=f(mk-n)$
114404
For which positive integer values of $n$ does $a|mn-b?$
28927
IMO 1987 - function such that $f(f(n))=n+1987$
39739
Fibonacci identity: $f_{n+1}f_{n-1} = f_n^2 + (-1)^n$
47611
Integers and integer functions
115018
Continuous Fibonacci number F(n)
113360
How many injective functions $f:[1,...,m]\to{[1,...,n]}$ has no fixed point? $(m\le n)$
20199
Find a surjective function $f:\mathbb{N}\to \mathbb{Q}$
38882
If $n$ is a positive integer such that $n^3 − n − 6 = 0$, then, for every positive integer $m$ with $m \not = n$, $m^3 − m − 6 \not = 0$.
1711
Quadratic Recurrence : $f(n) = f(n-1) + f(n-2) + f(n-1) f(n-2)$ Solution? How?
83784
Fixed Point of $x_{n+1}=i^{x_n}$
113329
Let $S=\{1,2,3,4,\dotsc,N\}$ and $X=\{ f: S \rightarrow S \mid x < y \Rightarrow f(x)\leqslant f(y)\}$. Then $|X|$ is equal to what?
81267
A simple doubt in number theory problem.
75448
Find all function satisfying $f(f(n))+f(n)=2n+3k$
28111
Let $f:[1,10]\to \Bbb{Q}$ be a continuous function and $f(1)=10,$then $f(10)=?$