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Number theory problem divisible

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    Prove that n ℂ Z+ is divisible by 3( respectively 9). to show that if and only if the sum of its digits is divisible by 3

    2. Relevant equations

    3. The attempt at a solution

    so n= 3q, q>3 that n[itex]\equiv[/itex]0 mod 3
    n=X1* 10^n+ x2*10^n-1......Xn
    so need to prove(x1+x2+......Xn)[itex]\equiv[/itex]0 mod 3, the how to prove the next step
  2. jcsd
  3. Jan 29, 2012 #2


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    Show 10^k=1 mod 3.
  4. Jan 29, 2012 #3


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    and for extra credit, google "casting out nines" for a better explanation of why this works (the same theorem holds for the number 9, in fact, for the same reason).
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