Hi, need a some help with this proof.

Prove the multiplicative order of is for odd prime .

How do I go about this?

Thank You for any help.

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- Sep 29th 2011, 05:08 AMalexgeek101Multiplicative order
Hi, need a some help with this proof.

Prove the multiplicative order of is for odd prime .

How do I go about this?

Thank You for any help. - Sep 29th 2011, 07:19 AMymarRe: Multiplicative order
You have to try first. What is the definition of the multiplicative order?

- Sep 29th 2011, 08:51 AMDevenoRe: Multiplicative order
step one: what is ? justify your answer.

- Oct 1st 2011, 05:22 AMalexgeek101Re: Multiplicative order
- Oct 1st 2011, 09:14 AMDevenoRe: Multiplicative order
try expanding using the binomial theorem. which terms don't have in them?

- Oct 1st 2011, 09:35 AMalexgeek101Re: Multiplicative order
- Oct 1st 2011, 09:43 AMDevenoRe: Multiplicative order
um, no....

the coefficent of p in the expansion is p:

where all the remaining terms involve higher powers of p.

thus .

so the multiplicative order of p+1 (mod p^2) has to divide p. what are our choices, given that p is an odd prime? - Oct 1st 2011, 09:49 AMalexgeek101Re: Multiplicative order
- Oct 1st 2011, 10:00 AMDevenoRe: Multiplicative order
almost...why isn't the order of p+1, 1 (after all, 1 divides p)?

it's a small detail, and easily answered, but it never hurts to dot the "i's" and cross the "t's". - Oct 1st 2011, 10:05 AMalexgeek101Re: Multiplicative order