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Multiple of prime p + multiple of (integer<p) = 1 proof?

  1. Dec 14, 2009 #1
    Let p be a prime number and x be some positive integer less than p.

    How do I prove that there exist integers a and b such that
    1 = ax + bp
  2. jcsd
  3. Dec 14, 2009 #2
    Hint: compare what you have with what you need.
  4. Dec 15, 2009 #3
    Since any term less than p is relatively prime to p, and thus has a solution of 1; it is easy to choose a desireable case.
    Last edited: Dec 15, 2009
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