US-TST 2002 Problem 2

Let $p>5$ be a prime number. For any integer $x$ , define $${f_p}(x) = \sum_{k=1}^{p-1} \frac{1}{(px+k)^2}$$ Prove that for any pair of positive integers $x$ , $y$ , the numerator of $f_p(x) - f_p(y)$ , when written as a fraction in lowest terms, is divisible by $p^3$ .