Question 89
Let $Q^+$ denote the set of positive rational numbers, and $\mathbb{Z}$ denote the set of all integers. Find all functions $f: Q^+ \to \mathbb{Z}$ that satisfy the conditions $f(1/x) = f(x)$ and $(x+1)f(x-1) = x f(x)$ for all $x \in Q^+$ such that $x \gt 1$.