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Oh i love these brain exercises!

  1. Jun 20, 2004 #1
    if x and y are pos. int. then rx >=y. x is an int. help!
     
  2. jcsd
  3. Jun 20, 2004 #2

    Gokul43201

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    What is the question ?

    If x, y are positive integers, there can always be found an r such that rx >= y. (Why repeat "x is an integer" ?) Do you want a proof of the above statement ?
     
  4. Jun 20, 2004 #3

    Gokul43201

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    Assume that y > rx , for all r

    Then the set S = {y-rx| r in Z+} consists only of positive numbers. So, S must possess a least element, say y-mx.

    But y-(m+1)x also belongs in S, since m+1 is in Z+ if m is.

    y-(m+1)x = y-mx - x < y - mx, since x>0, contrary to our choice of the minimal element - a contradiction !

    Hence, the assumption was false.
     
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