Question 71
Find all pairs $(f,g)$ of functions from the positive integers to the positive integers such that for every positive integer $n$,
$$f^{g(n)+1}(n)+g^{f(n)}(n)=f(n+1)-g(n+1)+1.$$
Here $f^1(n)=f(n)$ and $f^{k+1}(n)=f(f^k(n))$.
$$f^{g(n)+1}(n)+g^{f(n)}(n)=f(n+1)-g(n+1)+1.$$
Here $f^1(n)=f(n)$ and $f^{k+1}(n)=f(f^k(n))$.