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Distribution of power congruence classes

  1. Feb 22, 2012 #1
    Hi, I need help to prove this for my professor
    this is called "Distribution of power congruence classes" or something like that

    With all n∈NiS∈N correct
    1) n ≡Qs(n)(mod 10s-1)
    2) n ≡Qs(n)(mod 10s+1)

    http://img546.imageshack.us/img546/8341/withall.png [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Feb 23, 2012 #2

    Stephen Tashi

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    Science Advisor

    Your question isn't clear.

    You must explain your notation. What is [itex] N_i [/itex]? What is [itex] Q_s(n) [/itex]? What is [itex] Q'_s(n) [/itex] ?

    Instead of "correct", perhaps you mean "it is true that".
  4. Feb 23, 2012 #3
    Yes, I need to proove, that this is correct.
    To seperate [itex] Q_s(n) [/itex] and [itex] Q'_s(n) [/itex], I used apostrophe '
    I dont know, professor just gave this for us in a middle of Modular arithmetic class
    Last edited: Feb 23, 2012
  5. Feb 23, 2012 #4
    Can we perhaps decipher the question as follows:

    Let n and s be positive integers, let Qs(n) be the sum of the numbers formed by the digits of n in groups of s, starting from the right, and let Qs'(n) be the alternating such sum.

    Show that Qs(n)[itex]\equiv[/itex]n (mod 10s-1) and Qs'(n)[itex]\equiv[/itex]n (mod 10s+1)
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