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Given a positive integer $a$, a function $f$ from $\mathbb{N}$ to $\mathbb{R}$ satisfies $f(a)=f(1995)$, $f(a+1)=f(1996), f(a+2)=f(1997)$ and
$f(n+a)=\frac{f(n)-1}{f(n)+1} \text { for all } n \in \mathbb{N} .$
(a) Prove that $f(n+4 a)=f(n)$ for all $n$.
(b) Determine the smallest possible value of $a$.
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