1962 AHSME Problems/Problem 22: Difference between revisions
No edit summary |
|||
| (One intermediate revision by one other user not shown) | |||
| Line 7: | Line 7: | ||
==Solution== | ==Solution== | ||
<math>121_b</math> can be represented in base 10 as <math>b^2+2b+1</math>, which factors as <math>(b+1)^2</math>. | |||
Note that <math>b>2</math> because 2 is a digit in the base-b representation, but for any | |||
<math>b>2</math>, <math>121_b</math> is the square of <math>b+1</math>. <math>\boxed{\textbf{(D)}}</math> | |||
Latest revision as of 15:27, 16 April 2014
Problem
The number 
, written in the integral base 
, is the square of an integer, for
Solution
can be represented in base 10 as 
, which factors as 
.
Note that 
because 2 is a digit in the base-b representation, but for any
, is the square of 
. 
