+0  
 
0
671
2
avatar

what is biggest 4 digit number in base 23

 Jan 28, 2015

Best Answer 

 #2
avatar+26367 
+10

What is biggest 4 digit number in base 23 ?

$$\small{\text{
The biggest 4 Digit number in base 23 is:
}} \\
\small{\text{
$
22*23^3+22*23^2+22*23^1+22*23^0 = 23^4-1 = 279840
$
}} \\\\
\small{\text{
Geometric sequence:
$
s_4 = \dfrac{ a * (r^4-1) } { (r-1) }
\quad a = 22, \ \quad r = 23 \qquad s_4 = \frac{ 22 * (23^4-1) } { ( 23-1) } = \frac{ 22 * (23^4-1) } { ( 22 ) } = (23^4-1)
$
}}$$

 Jan 28, 2015
 #1
avatar+33616 
+10

23^4 - 1 or

 

$${{\mathtt{23}}}^{{\mathtt{4}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{279\,840}}$$

 

This answer is in base ten of course!

 Jan 28, 2015
 #2
avatar+26367 
+10
Best Answer

What is biggest 4 digit number in base 23 ?

$$\small{\text{
The biggest 4 Digit number in base 23 is:
}} \\
\small{\text{
$
22*23^3+22*23^2+22*23^1+22*23^0 = 23^4-1 = 279840
$
}} \\\\
\small{\text{
Geometric sequence:
$
s_4 = \dfrac{ a * (r^4-1) } { (r-1) }
\quad a = 22, \ \quad r = 23 \qquad s_4 = \frac{ 22 * (23^4-1) } { ( 23-1) } = \frac{ 22 * (23^4-1) } { ( 22 ) } = (23^4-1)
$
}}$$

heureka Jan 28, 2015

4 Online Users

avatar
avatar