Question 23
(IND 2) Let $f$ and $g$ be two integer-valued functions defined on the set of all integers such that
(a) $f(m+f(f(n)))=-f(f(m+1)-n$ for all integers $m$ and $n$;
(b) $g$ is a polynomial function with integer coefficients and $g(n)=g(f(n))$ for all integers $n$.
Determine $f(1991)$ and the most general form of $g$.
(a) $f(m+f(f(n)))=-f(f(m+1)-n$ for all integers $m$ and $n$;
(b) $g$ is a polynomial function with integer coefficients and $g(n)=g(f(n))$ for all integers $n$.
Determine $f(1991)$ and the most general form of $g$.