Find all $f$ such that $f(x+y)=f(x)f(y)f(xy)$ for all $x,y \in \mathbb{R}$
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
144222
If $f(x + 1) + f(x − 1) = f(x), \forall x \in \mathbb{R}$,then how to find $k$ such that $f(x + k) = f(x)$?
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
53024
$f(x)f(1/x)=f(x)+f(1/x)$
19019
Find all functions $f:\Bbb{Q}\rightarrow \Bbb{Q}$ such that $f(x)+f(t)=f(y)+f(z)$ for all rational numbers $x<y<z<t$ that form an AP
132093
Solve $f(f(x))=f(x)$
48592
Prove that $f'$ exists for all $x$ in $R$ if $f(x+y)=f(x)f(y)$ and $f'(0)$ exists
82597
How to find $ f(x)$ if $f(1-f(x))=x$ for all $x$ $\in \mathbb{R}$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.
41226
Find $f:f(xf(x)+f(y))=f(x)^2+y$
34343
Determine all $f : \mathbb R \rightarrow \mathbb R$ such that $f(f(x) + y) = f(x^2 - y) + 4yf(x)$.
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
32432
Strategies to find the set of functions $f:\mathbb R\to\mathbb R$ satisfing the functional equation: $f(x^3)+f(y^3)=(x+y)(f(x^2)+f(y^2)-f(xy))$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
98255
Find $f(x)$ such that $f(f(x)) = x^2 - 2$
125788
A function with a property $f(x+y)=f(x)f(y)$
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$