Find all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $yf(x)+xf(y)=(x+y)f(x^2+y^2)$
1071
Determine all functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that $xf(y)+yf(x)=(x+y)f(x^2+y^2)$ for all $x,y\in\mathbb{N}$ (contest question)
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
14975
Functions satisfying $f:\mathbb{N}\rightarrow\ \mathbb{N}$ and $f(f(n))+f(n+1)=n+2$
117793
Finding a function $\mathbb{N} \to \mathbb{N}$ that is surjective but not injective.
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
24810
Functions satisfying $(b-a)f'(\tfrac{a+b}{2}) = f(b)- f(a)$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?
17175
Problem in solving functional equation $f(x^2 + yf(x)) = xf(x+y)$
98363
Expanding two-variable function $f(x,y)$ over the complete sets $\{ g_{i}(x) \}$ and $\{ h_{j}(y) \}$
55286
Functional equation: $f: \mathbb{R} \rightarrow \mathbb{R}$, $f((x + 1) f(y)) = y (f(x) + 1)$
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
44293
Functions satisfying $f\left( f(x)^2+f(y) \right)=xf(x)+y$
39090
Finding functions such that $f(g(x)) = f(x)g(x)$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
11828
continuous functions on $\mathbb R$ such that $g(x+y)=g(x)g(y)$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$