Question 89
Let $m$ be a positive integer, $A=\{-m,-m+1, \ldots, m-1, m\}$ and $f: A \rightarrow A$ be a function such that $f(f(n))=-n$ for every $n \in A$.
a) Prove that the number $m$ is even.
b) Find the number of all functions $f: A \rightarrow A$ with the required property.
a) Prove that the number $m$ is even.
b) Find the number of all functions $f: A \rightarrow A$ with the required property.