Distribution of power congruence classes

[dec]

Hi, I need help to prove this for my class
this is called "Distribution of power congruence classes" or something like that

With all n∈N_iS∈N correct
1) n ≡Q_s(n)(mod 10^s-1)
2) n ≡Q‘_s(n)(mod 10^s+1)

 

[SlipEternal]

I have no clue what you are asking. What is \(\displaystyle Q_S(n)\)? What is \(\displaystyle N_i\)? What is \(\displaystyle N\)? For the latter two, do you mean \(\displaystyle \mathbb{N}_i\) and \(\displaystyle \mathbb{N}\)? Even still, I have no clue what \(\displaystyle Q_S(n)\) is.