Let $\frac mn$ be a fraction, where $m$ and $n$ are positive integers. Consider the operation defined by replacing $\frac mn$ by $\frac{m+

Let  be a fraction, where  and  are positive integers. Consider the operation defined by replacing  by  and then writing the result in lowest terms. For example, applying this operation to  would give  How many times must this operation be repeatedly applied to  before we obtain