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Determine if the following problem is symmetric and transitive

  1. Dec 10, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose ~ is defined on the whole numbers by a~b iff ab2 is a perfect cube. Determine if ~ is
    symmetric
    transitive

    2. Relevant equations
    ab2 must ba2


    3. The attempt at a solution

    I tried using different numbers, but it isn't coming out as a perfect square.

    For example, I said a=1
    b=0.................................. Then this works.
    Using other numbers it fails.

    Should a=b?
     
  2. jcsd
  3. Dec 10, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Meager! Welcome to PF! :smile:
    Hint: write a and b as a product of their prime factors. :wink:
     
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