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In need of direction

  1. Jun 19, 2004 #1
    i need some help here. i need to show that x=2k+1 and y=9k+4. i need to show that x and y are relatively prime. i am thinking of setting one = to k, and then substitiuting that into the otehr formula. any other suggestions?
     
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  3. Jun 19, 2004 #2

    matt grime

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    y-4x=k

    hence d:=(x,y)|k

    but d|x=2k+1 => d|1
     
  4. Jun 19, 2004 #3

    Gokul43201

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    What matt means is the following (in case it needs clarification) :

    Assume there is some number, d that divides y and x.

    Then d should also divide any linear combination of y and x, in particular y-4x.

    But since y-4x = k, this means that d divides k. So d should also divide 2k.

    But since x=2k+1, d also divides 2k+1

    The last two statements say that d divides 2k and 2k+1, which means that d should divide 1.

    So, the only number that divides both x and y is 1.
     
  5. Jun 19, 2004 #4
    o my that makes so much sense now. i was just setting one = to a k and then substitiuting it in the other. thank you both!
     
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