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Number theory/ divisibility

  1. Sep 16, 2010 #1
    {SOLVED}Number theory/ divisibility

    Show that m^2 is divisible by 3 if and only if m is divisible by 3.

    MY attempt:

    I assumed that 3k=m for some integers k and m.
    squared both sides and now get.

    3n=m where n=3*(3k^2). Thus 3|m^2

    Now the problem is when i assume:
    3k=m^2 and need to show 3|m.
     
    Last edited: Sep 16, 2010
  2. jcsd
  3. Sep 16, 2010 #2
    The easiest way seems to be via contradiction. If 3k = m^2 but 3 does not divide m, then what do you know about the prime factorization of m^2?
     
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