Problem - 161
Find the ordered pair of positive integers $(x, y)$ with the largest possible $y$ such that $\frac{1}{x} - \frac{1}{y}=\frac{1}{12}$ holds.
Solve $y$ with respect to $x$ gives $y=-12+\frac{144}{12-x}$. This means $(12-x)$ divides $144$. To make $y$ as large as possible, $(12-x)$ must be as small as possible. Hence, we find the solution to be $\boxed{(11, 132)}$.