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Homework Help: Rule of 9 proof

  1. Feb 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove the following
    a is congruent to s(mod 9)

    2. Relevant equations

    a=d0+ d110+ d2102+...+dr10r

    s= d0+ d1 +...+dr

    3. The attempt at a solution

    we know that 10-1=9 so we can say that 10 is congruent to 1(mod 9)

    so we know that a is congruent to d0+ d110+ d2102+...+dr10r which is congruent to d0+ d1+ d2+...+dr (mod 9).

    Is this a step in the right direction? Does anything else need to be shown?
  2. jcsd
  3. Feb 18, 2010 #2


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    Not much else needs to be shown. You could fill in some details, like saying why 10^2, 10^3 etc are also congruent to 1 mod 9. But I'm guessing you've got the idea.
    Last edited: Feb 18, 2010
  4. Feb 18, 2010 #3
    I guess what I was trying to ask was is the way I wrote a valid formal proof?
  5. Feb 18, 2010 #4


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    You wrote a valid INFORMAL proof. I.e. one where you don't detail all of the reasons for every step. If you want a formal proof, you should supply those reasons.
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