How to prove the following theorem. Could you explain.
Given the number $A = \langle a_n, a_{n-1}, \dots, a_0 \rangle_{10}$ and the modulus $m$ such that $(10, m) = 1$ from the sequence $b_1$,...,$b_n$ ($0 \leq b_i < m$ and $i = 1, \dots, n$) as follows D$a_0$ + $a_1$ is congruent to $b_1$ (mod m) D$b_0$ + $a_2$ is congruent to $b_2$ (mod m) and so on ...
D$b_(n-1)$ + $a_n$ is congruent to $b_n$ (mod m).
Thank you.
Here D is fixed in such a way, such that 10D is congruent to 1 (mod m)