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Proof for divisability tests

  1. Oct 12, 2008 #1
    what is the proof for divisibility tests in general, and in particular how are they derived.
    for example, i know that in base m, if the sum of the digits are a multiple of m-1, then m-1 is a factor. how tests like alternating digits having equal sums found?
    does a test exist for every number?
     
  2. jcsd
  3. Oct 12, 2008 #2

    CRGreathouse

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    Divisibility tests in a given base are just special cases of modular arithmetic. Examples (base 10) for adding digits and alternating digits: 10a + b = a + b (mod 9), 100a + 10b + c = a - b + c (mod 11).
     
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