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Math Help - Associates

  1. #1
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    Associates

    Hello all,

    My book gave a theorem that stated that if a and a' both divide x and y, and that every g that divides x and y also divides a and a', then a and a' are associates.

    Can anyone prove this?
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Samson View Post
    Hello all,

    My book gave a theorem that stated that if a and a' both divide x and y, and that every g that divides x and y also divides a and a', then a and a' are associates.

    Can anyone prove this?
    a and a' are both gcd's of x and y. What does this tell you?
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  3. #3
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    Does this mean that a = a'?
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  4. #4
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Samson View Post
    Does this mean that a = a'?
    Since a divides every other element that divides x and y, a must divide a'.

    The same reasoning shows a' divides a.

    Thus a and a' are associates by definition.
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  5. #5
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    Thank you!
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