If $f: N\rightarrow N $ be such that $f(f(n))+f(n+1)=n+2$ for all $n\in N$ find $f(1)$ and $f(2)$.
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
28007
Assuming: $\forall x \in [0,1]:f(x) > x$ Prove: $\forall x \in [0,1]:f(x) > x + \varepsilon $
9587
If $f(t) = 1+ \frac{1}{2} +\frac{1}{3}+....+\frac{1}{t}$, find $\sum^n_{r=1} (2r+1)f(r)$ in terms of $f(n)$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
37976
Find all functions $f$ such that $(x+y)f(x)+f(y^2)=(x+y)f(y)+f(x^2)$
63750
let $f(\frac{x}{3})+f(\frac{2}{x})=\frac{4}{x^2}+\frac{x^2}{9}-2$ then find $f(x)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
111756
How do I prove that then $f(x) = 1$ for some $x ∈ [0, 1]$?
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
14648
Show that $f_0 - f_1 + f_2 - \cdots - f_{2n-1} + f_{2n} = f_{2n-1} - 1$ when $n$ is a positive integer
52858
Find $f$ if $ f(x)+f\left(\frac{1}{1-x}\right)=x $
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
133333
Find $f(x)$ for $f(f(x))=\sin x$
91947
Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
57416
Fibonacci identity: $f_{n-1}f_{n+1} - f_{n}^2 = (-1)^n$