In the book it said, let
\displaystyle f(x)=\frac{x^{p-1}}{(p-1)!}(1-x)^p(2-x)^p\cdots (n-x)^p
where p is a prime number and p>n. Then it said that when i\ge p, the coefficients of f^{(i)} (x) are multiples of p. I can't see why it is true. Can someone elaborate? Thanks.