Question 113
Find all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ satisfying the following two conditions:
(i) for all integers $x$ we have $f(f(x))=x$;
(ii) for all integers $x$ and $y$ such that $x+y$ is odd we have $f(x)+f(y) \geq x+y$.
(i) for all integers $x$ we have $f(f(x))=x$;
(ii) for all integers $x$ and $y$ such that $x+y$ is odd we have $f(x)+f(y) \geq x+y$.