fairly easy, routine function, from Q+ to Q+
Source: China TST 2007 Q4
February 21, 2008
functioninductionalgebra proposedalgebra
Problem Statement
Find all functions f: \mathbb{Q}^{\plus{}} \mapsto \mathbb{Q}^{\plus{}} such that:
f(x) \plus{} f(y) \plus{} 2xy f(xy) \equal{} \frac {f(xy)}{f(x\plus{}y)}.