NMC 1996 Problem 4

The real-valued function $f$ is defined for positive integers, and the positive integer a satisfies

$$\begin{gathered} f(a)=f(1995), f(a+1)=f(1996), f(a+2)=f(1997) \\ f(n+a)=\frac{f(n)-1}{f(n)+1} \text { for all positive integers } n \end{gathered}$$

(i) Show that $f(n+4 a)=f(n)$ for all positive integers $n$. (ii) Determine the smallest possible $a$.