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Math Help - greatest common divisor

  1. #1
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    greatest common divisor

    ok i'm trying to do 2 proofs for gcd

    show that if ax + by =1 then gcd(a,b)=1

    and

    gcd(a,a+k) divides k

    just need a little hint on where to start
    thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by action259 View Post
    ok i'm trying to do 2 proofs for gcd

    show that if ax + by =1 then gcd(a,b)=1
    Suppose c>1 is the gcd(a,b), then c divides (ax+by), but c does not
    divide 1, a contradiction.

    and

    gcd(a,a+k) divides k
    let c be the gcd(a, a+k), then by definition c divides a, and c divides a+k.

    RonL
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