Let $\displaystyle \frac{m}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \mbox{...} + \frac{1}{p-1} $ . $\displaystyle p $ is a prime number > 2 . Prove that $\displaystyle m $ is divisible by $\displaystyle p $. If $\displaystyle p > 3 $, Prove that $\displaystyle m $ is divisible by $\displaystyle p^2 $.

I've done the first bit, I can't seem to get ideas for the 2nd part of the problem. Please help! :)