- Thread starter
- #1

- Apr 13, 2013

- 3,839

We consider the usual representation of non-negative integers, where the digits correspond to consecutive powers of the basis in a decreasing order.

Show that at such a representation, for the conversion of a number with basis $p$ to a system with basis $q$, where $p=q^n$ and $n$ positive integer, it suffices that each digit of the number is expressed from initial system of basis $p$ to the system of basis $q$, using $n$ digits of the system of basis $q$.

Also the rule should be stated and it should be proved at the reverse case, i.e. when the conversion is done from the system of basis $q$ to the system of basis $p$.

Could you give me a hint how we could show this?