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# Rings

Maths and statistics discussion, revision, exam and homework help.

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1. Rings
A bit of a proof that I don't understand again.
First of all I'll state the theorem
If where and p is prime then .
Starting about halfway through it says this, "Suppose p divides a ( ). Then and ." Why is if p divides a?
EDIT: IF more information is needed let me know, I'm just too lazy to type it all out if it is not needed.
Last edited by JBKProductions; 13-05-2012 at 23:10.
2. Re: Rings
maybe im missing something here but if a=pa' then p^k-1a=p^ka'
3. Re: Rings
(Original post by JBKProductions)
A bit of a proof that I don't understand again.
First of all I'll state the theorem
If where and p is prime then .
Starting about halfway through it says this, "Suppose p divides a ( ). Then and ." Why is if p divides a?
I think because
4. Rings
Ok thanks, I understand it now.
5. Re: Rings
I have attached the proof here, can someone explain the last part to me, I'm not sure exactly why there are exactly p^{k-1} elements divisible by p.
Last edited by JBKProductions; 14-05-2012 at 21:50.
6. Re: Rings
(Original post by JBKProductions)
I have attached the proof here, can someone explain the last part to me, I'm not sure exactly why there are exactly p^{k-1} elements divisible by p.
Think about what is: it's (essentially) the remainder that you get when you divide an integer by ; that is . How many of these are divisible by ? Well you have . (Note that .)

How many of these are there?
Last edited by nuodai; 14-05-2012 at 00:46.
7. Re: Rings
(Original post by nuodai)
Think about what is: it's (essentially) the remainder that you get when you divide an integer by ; that is . How many of these are divisible by ? Well you have . (Note that .)

How many of these are there?
EDIT: I understand it now, thanks.
Last edited by JBKProductions; 14-05-2012 at 01:21.

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Last updated: May 14, 2012
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