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-   -   Distribution of power congruence classes (http://www.physicsforums.com/showthread.php?t=580211)

dec178 Feb22-12 10:31 AM

Distribution of power congruence classes
 
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

Stephen Tashi Feb23-12 12:07 AM

Re: Distribution of power congruence classes
 
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".

dec178 Feb23-12 12:46 AM

Re: Distribution of power congruence classes
 
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

Norwegian Feb23-12 01:43 AM

Re: Distribution of power congruence classes
 
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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