Let \(\frac{m}{n}\) be a fraction, where \(m\) and \(n\) are positive integers. Consider the operation defined by replacing \(\frac{m}{n}\) by \(\frac{m+1}{n+1}\) and then writing the result in lowest terms. For example, applying this operation to \(\frac{5}{14}\) would give \(\frac{2}{5}\). How many times must this operation be repeatedly applied to \(\frac{1}{2005}\) before we obtain \(\frac{2004}{2005} \).
