finding the functions satisfying $f(xy)=f(x)f(y)-f(x+y)+1$
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
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
139436
Show function $f(x,y)=(x^2-y^2,2xy)$ is $1$-$1$ by Inverse Function Theorem
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)
32856
Functional equations $f(x+y)= f(x) + f(y)$ and $f(xy)= f(x)f(y)$
88683
Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
6680
Solve for all possible functions f: $|f(x)-f(y)|=2|x-y|$.
103251
Solution(s) to $f(x + y) = f(x) + f(y)$ (and miscellaneous questions...)
409
functions satisfying $f(x - y) = f(x) f(y) - f(a - x) f(a + y)$ and $f(0)=1$
81720
$f(x) + f(x+f(y)) = y + f(f(x) + f(f(y)))$
50552
find functions that $f(m+k)=f(mk-n)$
153942
Solution of functional equation $f(x+y)=f(x)+f(y)+y\sqrt{f(x)}$
44670
Find all functions $f: \mathbb Z \to \mathbb Z$ such that $f(x+y)=f(x)+f(y)$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
148227
Rewriting of functional equation $f(xy)=f(x)+f(y)$
49211
Solving $f(x+y) = f(x)f(y)f(xy)$
111556
Solving functional equation $f(x+y)+f(x-y)=2f(x)\cos y$?