MathDB

Let Q^\plus{} denote the set of positive rational numbers. Show that there exists one and only one function f: Q^\plus{}\to Q^\plus{} satisfying the following conditions: (i) If

0<q<1/2

then f(q)\equal{}1\plus{}f(q/(1\minus{}2q)), (ii) If

1<q\le2

then f(q)\equal{}1\plus{}f(q\minus{}1), (iii) f(q)\cdot f(1/q)\equal{}1 for all q\in Q^\plus{}.

Problem Statement