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Find the smallest positive integer B so that when we express the decimal number 301 as a base B number, we still get a 2-digit number.

 Sep 30, 2024
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Find the smallest positive integer B so that when we express the decimal number 301 as a base B number, we still get a 2-digit number.   

 

Well, in base 10 it's a three digit number, so the base has to be bigger than ten.  

 

Per https://www.rapidtables.com/convert/number/base-converter.html it's base 18 ... 30110 = GD19    

 

For information, the next one down was 17 ... 31010 = 10C17    

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 Oct 1, 2024

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