Functions which satisfy $f(m^2+n^2)=f(m)^2+f(n)^2$
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
122329
Determine all functions $f(x)$ such that $f(f(x+y))=f(x)+f(y)$
100816
Mandelbrot-like sets for functions other than $f(z)=z^2+c$?
137218
Does there exist a polynomial $f(x)$ with real coefficients such that $f(x)^2$ has fewer nonzero coefficients than $f(x)$?
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
54604
Evaluate $ \sum_{m > n > 0} \frac{m^2 - n^2}{(m^2 + n^2)^2} $
105497
A function satisfying a series equation
80210
It is posible to have a function $f$ with the following property?
13248
How to obtain $f(x)$, if it is known that $f(f(x))=x^2+x$?
141938
Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$
5419
Continuous functions with $f^2(x)=g^2(x)\neq 0$
44717
Does there exist a bijective $f:\mathbb{N} \to \mathbb{N}$ such that $\sum f(n)/n^2$ converges?
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
14495
I need to find all functions $f:\mathbb R \rightarrow \mathbb R$ which are continuous and satisfy $f(x+y)=f(x)+f(y)$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
3801
Functions that take rationals to rationals
28620
Function $f(z)$ such that $|f(z)| > |z|$ for every $z\in\mathbb{C}, 1/f(z)$