# Prove q-ary representation of n*q

Robb
Homework Statement:
Let ##q \geq 2## be an integer. Let ##n = (d_k d_{k-1} \dots d_1 )_(q)## be a q-ary representation of n. Prove that ##nq = (d_k d_{k-1} \dots d_1 0)_(q)##.
Relevant Equations:
as above for n and nq.
##nq = q(d_1 + d_2 q + d_3 q^2 + \dots + d_k q^{k-1})##
##= d_1 q + d_2 q^2 + d_3 q^3 + \dots + d_k q^k##
##= d_k d_{k-1} \dots d_1 0##
Can someone please explain how to get from line two to line three. This is instructors solution and not sure I understand. Thanks!

## Answers and Replies

Mentor
2022 Award
In a q-ary representation, we have the lowest digit for ##q^0## and we have to note it. You can always make easy examples with ##q=10## and any numbers you want.

Robb