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Math Help - Proofs of rules of divisibility

  1. #1
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    Proofs of rules of divisibility

    Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11 using modular arithmetic if possible.

    I don't really get the proofs I searched from the net. Thanks!
    Last edited by cookiejar; January 24th 2010 at 12:06 AM.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Hi! Can anybody pls prove the rules of divisibility for 4, 5,6,9, & 11
    Can you be more specific? . I'm not quite sure what you mean. Do you want to look at residu-classes modulo - these numbers?
    Last edited by Dinkydoe; January 24th 2010 at 11:08 AM.
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  3. #3
    Moo
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    Proofs of divisibility, do you mean :

    - 4 : last two digits form a number which is a multiple of 4
    - 5 : ends by 0 or 5
    - 6 : multiple by 2 & 3
    - 9 : sum of digits makes a multiple of 9
    - 11 : difference of alternate sums is a multiple of 11

    ?

    If so, what specifically don't you understand ?
    For 4, write the number as 100k+..
    For 5, write the number as 10k+.
    For 6, chinese remainder theorem
    For 9, write the number as a linear combination of powers of 10, and while working modulo 9, it should be obvious
    For 11, same thing as 9
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