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Math Help - the possible values of gcd(a; a + prime).

  1. #1
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    the possible values of gcd(a; a + prime).

    If p is a prime, find the possible values of gcd(a, a + p).

    and find a necessary and sufficient condition for gcd(a, a+p) = 1 where p is a
    prime.
    Last edited by zhushp; November 8th 2009 at 12:10 AM.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    If d divides both a and a+p then d|p, so d=1 or d=p.

    A necessary and sufficient condition that \mbox{gcd }(a,a+p)=1 is that p\nmid a.
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