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Math Help - About Primes

  1. #1
    Junior Member
    Joined
    May 2009
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    74

    About Primes

    Hi evebody,

    Is there any proof of:

    Let P_1, P_2 two different primes

    Prove (or plz give me a link) that if

    <br />
a=P_1^s-P_2^s<br />

    then

    <br />
a \quad mod \quad P_1 \quad /= 0<br />

     <br />
a \quad mod \quad P_2 \quad /= 0<br />

    For every positive integer s

    (/= means not equal)

    Thank you a lot
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Thanks
    1
    a\equiv-p_2^s\,(\bmod\,p_1)\not\equiv0\,(\bmod\,p_1) as p_1 does not divide p_2.

    Similarly a\equiv p_1^s\,(\bmod\,p_2)\not\equiv0\,(\bmod\,p_2) as p_2 does not divide p_1.
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  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    74
    Indeed...
    I missed the spot that

    <br />
P^s \quad mod \quad P = 0<br />

    for any Prime P.

    Next time i will be more mindful.

    Thank you.
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