1992 Putnam A1

Prove that $f(n) = 1-n$ is the only integer-valued function
defined on the integers that satisfies the following conditions.

(i) $f(f(n)) = n$, for all integers $n$;

(ii) $f(f(n+2)+2) = n$ for all integers $n$;

(iii) $f(0) = 1$.

证明 $f(n) = 1-n$ 是唯一的整数值函数

定义在满足以下条件的整数上。

(i) $f(f(n)) = n$，对于所有整数 $n$；

(ii) 对于所有整数 $n$，$f(f(n+2)+2) = n$；

(iii) $f(0) = 1$。