Prove that if is an odd prime, prove that either or is divisible by 10.

My proof so far:

If , then we are done. Assume 10 doesn't divide .

Let p=2n+1 for some integer n. Then so 2 can divide it.

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- Jan 30th 2008, 09:34 AMtttcomraderOdd prime division problem
Prove that if is an odd prime, prove that either or is divisible by 10.

My proof so far:

If , then we are done. Assume 10 doesn't divide .

Let p=2n+1 for some integer n. Then so 2 can divide it. - Jan 30th 2008, 09:49 AMCaptainBlack
- Jan 30th 2008, 10:19 AMtttcomrader
So far our course have not introduce mod yet, is it possible to do this by other means? thank you.

- Jan 30th 2008, 02:48 PMThePerfectHacker
A number has one of the forms: .

Now examine each of these forms.

1) this is never prime.

2) this is only prime for , but the prime is**odd**so it cannot have this form.

3) since have no common factors this is a possible prime.

4) this is never prime.

5) this is only prime at and that prime is which cannot be because .

6) this is never prime.

7) a possible prime.

8) this is never prime.

9) a possible prime.

Which means has one of three forms: . If you substitute that into you will see it is divisible by . For example, so is divisible. And so on.

I just realized I forgot - but you get the idea. And do not be afraid of this argument, it might look long but that is because I explained it in detail.