16. [10] If $p$ and $q$ are positive integers and $\frac{2008}{2009}<\frac{p}{q}<\frac{2009}{2010}$, what is the minimum value of $p$ ?
Answer: 4017 By multiplying out the fraction inequalities, we find that $2008 q+1 \leq 2009 p$ and $2010 p+\leq 2009 q$. Adding 2009 times the first inequality to 2008 times the second, we find that $2008 \cdot 2009 q+4017 \leq 2008 \cdot 2009 q+p$, or $p \geq 4017$. This minumum is attained when $\frac{p}{q}=\frac{4017}{4019}$.