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Integer Problem

  1. Dec 16, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that 3 divides one of the integers n, n + 2, or n + 4, for any integer n.


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 16, 2008 #2

    Dick

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    Try, ok? Any integer n has a remainder of either 0, 1 or 2 when divided by 3. Come on.
     
  4. Dec 16, 2008 #3
    Okay...so whats the formula for proving that true is my question?

    Thanks
     
  5. Dec 16, 2008 #4

    Dick

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    Read the forum rules. You are supposed to put something in the "attempt at a solution section". I just gave you a hint. There really is no 'formula'.
     
  6. Dec 17, 2008 #5
    Let n be any such integer. THen by the division algorithm there exist integers q and r such that

    [tex] n=3q+r,[/tex]

    [tex]n+2=3q_1+r[/tex]

    [tex]n+4=3q_2+r[/tex] [tex]0\leq r<3[/tex]

    i.e r=0, 1 or 2

    Now, say if r=0, what happens? if r=1, what happens? if r=2 what happens?

    P.S. This is what Dick said, i just wanted to make a little bit easier on you.
    YOu MUST show your work next time.
     
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