Find all function $f:\Bbb{N}_0 \rightarrow \Bbb{N}_0 $ satisfying the equation $f(f(n) + f(n) = 2n +3k,$ where $k$ is a fixed natural number
75448
Find all function satisfying $f(f(n))+f(n)=2n+3k$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
11806
Functional equation.
14409
A problem about function N
62111
Functional Equation $f(mn)=f(m)f(n)$.
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
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
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
29403
Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
17604
What is a good asymptotic for $f_n = f_{n-1}+\ln(f_{n-1})$?
53745
Euler's $\phi$ function: Find all $n$ such that $\phi(n)=n/3$
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
144090
How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
131586
Hard functional equation: $ f \big ( x y + f ( x ) \big) = f \big( f ( x ) f ( y ) \big) + x $