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)
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 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
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)[itex]\equiv[/itex]n (mod 10^{s}-1) and Q_{s}'(n)[itex]\equiv[/itex]n (mod 10^{s}+1)