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A base-10 integer n can be represented as $32_a$ in one base and $13_b$ in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?

 Apr 10, 2021
 #1
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32a = 13b   means  3a + 2 = b + 3

 

b = 3a - 1

 

Smallest possible a is 4, so:  a = 4, hence  b = 11, and  a+b = 15

 Apr 10, 2021

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