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For what base is the representation of $285_{10}$ a four digit number whose final digit is odd?

 Apr 4, 2022
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For what base is the representation of $285_{10}$ a four digit number whose final digit is odd?

 

The base is obviously going to be between 2 and 9  (smaller than 10 because we need more digits)

Possibilities  2,3,4,5,6,7,8,9

now when you divide 285 by the new base you have to get an odd remainder.

So what possible bases could it be so far?  

After that, for the base you need I will call it b

\(b^3<285

 

So you can eliminate the ones that don't work till to hone in on the ones that do.

 Apr 4, 2022

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