Question 23
Find all functions $f:\mathbb Z\to\mathbb Z$ such that for all integers $a,b,c$ with $a+b+c=0$,
$$(a)^2+(b)^2+(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).$$
Here $\mathbb Z$ is the set of all integers.
$$(a)^2+(b)^2+(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).$$
Here $\mathbb Z$ is the set of all integers.