Problem

Source: Turkey TST 2009, Problem 1

Tags: function, algorithm, number theory, Euclidean algorithm, continued fraction, algebra, functional equation



Find all $ f: Q^ + \to\ Z$ functions that satisfy $ f \left(\frac {1}{x} \right) = f(x)$ and $ (x + 1)f(x - 1) = xf(x)$ for all rational numbers that are bigger than 1.