Distribution of power congruence classes

[dec178]

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]

Your question isn't clear.

You must explain your notation. What is $N_i$? What is $Q_s(n)$? What is $Q'_s(n)$ ?

Instead of "correct", perhaps you mean "it is true that".

 

[dec178]

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

 

[Norwegian]

Can we perhaps decipher the question as follows:

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

Show that Q_s(n)$\equiv$n (mod 10^s-1) and Q_s'(n)$\equiv$n (mod 10^s+1)