Difference between revisions of "1962 AHSME Problems/Problem 22"
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− | {{ | + | <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 .