What is biggest 4 digit number in base 23 ?
$$\small{\text{
The biggest 4 Digit number in base 23 is:
}} \\
\small{\text{
$
22*23^3+22*23^2+22*23^1+22*23^0 = 23^4-1 = 279840
$
}} \\\\
\small{\text{
Geometric sequence:
$
s_4 = \dfrac{ a * (r^4-1) } { (r-1) }
\quad a = 22, \ \quad r = 23 \qquad s_4 = \frac{ 22 * (23^4-1) } { ( 23-1) } = \frac{ 22 * (23^4-1) } { ( 22 ) } = (23^4-1)
$
}}$$
23^4 - 1 or
$${{\mathtt{23}}}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{279\,840}}$$
This answer is in base ten of course!
What is biggest 4 digit number in base 23 ?
$$\small{\text{
The biggest 4 Digit number in base 23 is:
}} \\
\small{\text{
$
22*23^3+22*23^2+22*23^1+22*23^0 = 23^4-1 = 279840
$
}} \\\\
\small{\text{
Geometric sequence:
$
s_4 = \dfrac{ a * (r^4-1) } { (r-1) }
\quad a = 22, \ \quad r = 23 \qquad s_4 = \frac{ 22 * (23^4-1) } { ( 23-1) } = \frac{ 22 * (23^4-1) } { ( 22 ) } = (23^4-1)
$
}}$$