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Math Help - GCD Proof

  1. #1
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    GCD Proof

    Assume GCD(n,b) = 1. Show that if n | ab then n | a.

    My professor says: Hint - Use Bezout's identy

    Thanks in advance for any help...
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  2. #2
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    Quote Originally Posted by jzellt View Post
    Assume GCD(n,b) = 1. Show that if n | ab then n | a.

    My professor says: Hint - Use Bezout's identy

    Thanks in advance for any help...

    Hint: You can use xn + yb = 1, where x,y are integers
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  3. #3
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    GCD(n,b) = 1 => there exist integers x,z s.t. 1 = nx + bz

    now multiply this by a and you'll get: a = anx + abz

    n will now divide anx (because of the n) and will divide abz (because of the assumption), so n will divide their sum, i.e. n will divide a.
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