Question 93
The functions $f(n) = n^2$ and $f(n) = -n^2$ both satisfy the following equations:
$$
f(f(n) + 1) - f(f(n) - 1) = 4n^2
$$
Either show that there is no other function $f : \mathbb{Z} \to \mathbb{Z}$ satisfying the above equation for all $n \in \mathbb{Z}$, or prove that another such function exists.
$$
f(f(n) + 1) - f(f(n) - 1) = 4n^2
$$
Either show that there is no other function $f : \mathbb{Z} \to \mathbb{Z}$ satisfying the above equation for all $n \in \mathbb{Z}$, or prove that another such function exists.