A problem with Joseph Rotman's Advanced modern Algebra

[qinglong.1397]

Homework Statement

Let $n=p^rm$, where $p$ is a prime not dividing an integer $m>1$. Prove that

$p$ does not divide $C_n^{p^r}$.

Homework Equations

There is a hint: Assume otherwise, cross multiply, and use Euclid's lemma.

The Attempt at a Solution

Although the author gives a hint, I still cannot figure out how to use it. I do not know what "cross multiply" means. Can anyone of you tells me? Or, can you give me another hint? Thank you very much!

 

[Stephen Tashi]

"Cross multiply" is slang for changing an equation like $\frac{a}{b} = \frac{c}{d}$ to the equation $ad = bc$. I suppose it could also be used to indicate changing an equation like $a = \frac{c}{d}$ to the form $ad = c$.