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Show that if 3 divides n^2, 3 divides n

  1. Mar 1, 2006 #1
    Show that if 3 divides n^2, 3 divides n. Hint: n can only be in the form 3a, 3a + 1, 3a + 2

    Can someone help me with this? It's pretty simple, I just don't know how to express it mathematically.
     
  2. jcsd
  3. Mar 1, 2006 #2

    mathman

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    Gold Member

    n2 then has three possibilities.
    9a2
    9a2+6a+1
    9a2+12a+4
    Only the first (for n=3a) is divisible by 3. The other two have a remainder of 1 after division by 3.
     
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