Converting Base $N$

Number Theory Level 3

$\Large 111_{n^3}$

If $n$ is a positive integer , What is the number above when written in base $n$ ?

303003 3003003 101001 300303 100101 1001001 None of These 10101

1 solution

Alex G
Jun 2, 2016

$111_{n^3} = 1 + n^3 + n^6$

Note that number $\overline{...gfedcba}$ in base n is equivalent to:

$a+bn+cn^2+dn^3+en^4+fn^5+gn^6...$

In the case in the problem, $a=1$ , $d=1$ , and $g=1$ . The answer is therefore

$\boxed{1001001}$