ILL 1978 Problem 43

If $p$ is a prime greater than $3$ , show that at least one of the numbers $$\frac{3}{p^2} , \frac{4}{p^2} , \cdots, \frac{p-2}{p^2}$$ is expressible in the form $\frac{1}{x} + \frac{1}{y}$ , where $x$ and $y$ are positive integers.