Put another way,

How do I show that p^3 divides r-s in this instance?

Results 1 to 3 of 3

- May 9th 2009, 10:09 PM #1

- Joined
- May 2008
- Posts
- 140

- May 11th 2009, 09:12 AM #2

- Joined
- May 2008
- Posts
- 140

- May 11th 2009, 09:30 AM #3

- Joined
- Apr 2009
- From
- Atlanta, GA
- Posts
- 409

## Wolstenholme's Theorem

Well, if , then . Since is prime, by Wolstenholme's Theorem, the numerator of is divisible by , and by definition, is the lowest positive integer ensuring the RHS is a whole number, essentially doing the job of canceling all the denominators: , for some and .

Therefore, the entire RHS is divisible by , hence

*Are you asking us to prove Wolstenholme's Theorem or to simply connect the dots enough to make use of this theorem?