# A problem with Joseph Rotman's Advanced modern Algebra

1. Sep 11, 2011

### qinglong.1397

1. The problem statement, all variables and given/known data

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

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

2. Relevant equations

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

3. 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!

2. Sep 11, 2011

### 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 $ad = c$.