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Math Help - Number Theory relatively prime.

  1. #1
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    Number Theory relatively prime.

    Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
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  2. #2
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    Quote Originally Posted by JCIR View Post
    Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
    Use the gcd algorithm to obtain (a+b, a-b) = (a-b, 2). Then you know that the gcd is 2 if a-b is even or 1 if a-b is odd.
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    Quote Originally Posted by JCIR View Post
    Let a and b be relatively prime numbers. prove that (a+b,a-b) is either 1 or 2.
    Hint: a-b = (a+b) - 2b.
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