Results 1 to 3 of 3

Math Help - Congruence and Euler's function

  1. #1
    Junior Member
    Joined
    Mar 2008
    Posts
    33

    Congruence and Euler's function

    Please help on following:

    Show if m>1 then a^m \equiv a^{m-\phi(m)}(mod \ m) for all natural numbers a.

    Basic Euler function is this  a^{\phi(m)} \equiv 1 (mod \ m) but how to build it up in order to answer the above question?

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    a^{\phi(m)} \equiv 1\implies a^{-\phi(m)}\equiv 1. Now multiply both sides by a^m. (Here negative exponents means inverses mod m).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2008
    Posts
    33
    I get it, thank you.
    Forgot about inverse.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euler Phi function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: October 19th 2011, 11:31 PM
  2. Euler Function phi(n)
    Posted in the Number Theory Forum
    Replies: 22
    Last Post: May 29th 2010, 07:29 AM
  3. Euler phi-function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 15th 2010, 02:38 PM
  4. Euler phi-Function
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 11th 2009, 06:11 PM
  5. Euler phi function
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: January 22nd 2009, 03:19 AM

Search Tags


/mathhelpforum @mathhelpforum