solving functional equation $f(x+y) +f(x)f(y)=f(x)+f(y)+f(xy)$ for all real numbers
118727
$g(x+y)+g(x)g(y)=g(xy)+g(x)+g(y)$ for all $x,y$.
29647
Do there exist functions satisfying $f(x+y)=f(x)+f(y)$ that aren't linear?
48925
BMO1 2009/10 Q5 functional equation: $f(x)f(y) = f(x + y) + xy$
69707
If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, then prove that $f(x) = 0$ for all $x ≤ 0$.
120170
A late-diverging "approximating solution" for a system of functional equations
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
65946
A function $f: \mathbb R \to \mathbb R$ satisfies equation $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb R $
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
47212
Solving functional equation
20568
Does the following have a solution for f(x,y)?
132093
Solve $f(f(x))=f(x)$
53024
$f(x)f(1/x)=f(x)+f(1/x)$
66772
$f(f(x)f(y))+f(x+y)=f(xy)$
69734
how to find all functions such that $f\left( x^{2} - y^{2} \right) = ( x - y )( f(x) + f(y) )$
116270
Functional equations leading to sine and cosine
128751
Solving for $f(2004)$ in a given functional equation