Distribution of power congruence classes

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Discussion Overview

The discussion revolves around the concept of "Distribution of power congruence classes" in modular arithmetic, specifically focusing on proving certain congruences involving integers and their digit sums. The scope includes theoretical exploration and clarification of notation used in the problem.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant seeks to prove two congruences involving an integer n and a function Q_s(n) related to the digit sums of n.
  • Another participant requests clarification on the notation used, specifically questioning the definitions of N_i, Q_s(n), and Q'_s(n).
  • A participant explains that Q_s(n) and Q'_s(n) are separated by an apostrophe, indicating they are distinct functions.
  • A later reply proposes a possible interpretation of the question, defining Q_s(n) as the sum of digits of n in groups of s and Q_s'(n) as the alternating sum of those groups, suggesting the congruences to prove.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the clarity of the original question or the definitions of the terms involved. Multiple interpretations and clarifications are presented without resolution.

Contextual Notes

Limitations include unclear definitions of the notation and the specific nature of the functions Q_s(n) and Q'_s(n), which may affect the understanding of the problem.

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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
 
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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".
 
Yes, I need to proove, that this is correct.
To separate [itex]Q_s(n)[/itex] and [itex]Q'_s(n)[/itex], I used apostrophe '
I don't know, professor just gave this for us in a middle of Modular arithmetic class
 
Last edited:
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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