Results 1 to 2 of 2

Math Help - Number theory question 3-3

  1. #1
    Member
    Joined
    Feb 2011
    Posts
    75

    Number theory question 3-3

    Show that if p is prime and m \equiv n(mod p-1), then for any integer
    a:

    a^{m}  \equiv a^{n} (mod p)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    Oct 2012
    From
    India
    Posts
    61
    Thanks
    3

    Re: Number theory question 3-3

    Use fermat's little theorem. Simply put, if m == n (mod (p - 1)), m - n = k(p - 1), for some integer k. Now, use both sides as powers of a, some number a. a^(k(p - 1)) can be written as (a^(p - 1))^k, where p is a prime.

    Salahuddin
    Maths online
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Number theory question 1-3
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 26th 2012, 03:01 AM
  2. Number theory question 2-3
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 26th 2012, 02:51 AM
  3. number theory question
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 21st 2009, 05:09 AM
  4. Number theory Question 1
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: January 14th 2009, 04:04 AM
  5. Number theory Question 2
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: January 14th 2009, 03:14 AM

Search Tags


/mathhelpforum @mathhelpforum