Results 1 to 3 of 3

Thread: About Primes

  1. #1
    Member
    Joined
    May 2009
    Posts
    77

    About Primes

    Hi evebody,

    Is there any proof of:

    Let$\displaystyle P_1, P_2$ two different primes

    Prove (or plz give me a link) that if

    $\displaystyle
    a=P_1^s-P_2^s
    $

    then

    $\displaystyle
    a \quad mod \quad P_1 \quad /= 0
    $

    $\displaystyle
    a \quad mod \quad P_2 \quad /= 0
    $

    For every positive integer s

    (/= means not equal)

    Thank you a lot
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member TheAbstractionist's Avatar
    Joined
    Apr 2009
    Posts
    328
    Thanks
    1
    $\displaystyle a\equiv-p_2^s\,(\bmod\,p_1)\not\equiv0\,(\bmod\,p_1)$ as $\displaystyle p_1$ does not divide $\displaystyle p_2.$

    Similarly $\displaystyle a\equiv p_1^s\,(\bmod\,p_2)\not\equiv0\,(\bmod\,p_2)$ as $\displaystyle p_2$ does not divide $\displaystyle p_1.$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2009
    Posts
    77
    Indeed...
    I missed the spot that

    $\displaystyle
    P^s \quad mod \quad P = 0
    $

    for any Prime P.

    Next time i will be more mindful.

    Thank you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. primes
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Apr 2nd 2010, 10:18 AM
  2. Primes
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Aug 8th 2009, 01:26 PM
  3. Primes
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Feb 12th 2009, 09:59 PM
  4. Help with primes
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Jan 20th 2009, 08:01 PM
  5. primes
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Oct 16th 2008, 12:21 AM

Search Tags


/mathhelpforum @mathhelpforum