Turkey TST 2009 Functional Equation
Source: Turkey TST 2009, Problem 1
April 5, 2009
functionalgorithmnumber theoryEuclidean algorithmcontinued fractionalgebrafunctional equation
Problem Statement
Find all f: Q^ \plus{} \to\ Z functions that satisfy f \left(\frac {1}{x} \right) \equal{} f(x) and (x \plus{} 1)f(x \minus{} 1) \equal{} xf(x) for all rational numbers that are bigger than 1.