Question 30
How many functions $f: \mathbb{Z} \rightarrow \mathbb{R}$ satisfy the following three properties?
(a) $f(1)=1$;
(b) For all $m, n \in \mathbb{Z}$, $f(m)^2 - f(n)^2 = f(m+n) f(m-n)$;
(c) For all $n \in \mathbb{Z}$, $f(n) = f(n+2013)$.
(a) $f(1)=1$;
(b) For all $m, n \in \mathbb{Z}$, $f(m)^2 - f(n)^2 = f(m+n) f(m-n)$;
(c) For all $n \in \mathbb{Z}$, $f(n) = f(n+2013)$.