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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.

 
 Jun 11, 2024
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For a number to be 2-digits in a certain base, the cub of the base must be more than the number. We can test out all numbeers until one works.

 

2^3 = 8 < 301

3^3 = 27 < 301

4^3 = 64 < 301

5^3 = 125 < 301

6^3 = 216 < 301

7^3 = 343 > 301

 

This means that 7 is the smallest value for B that works.

 Jun 11, 2024

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