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A base-10 integer n can be represented as \( 32_a\) in one base and \(23_b\) in another base, where a and b are any integer bases larger than 3. What is the smallest possible sum a+b?

 Sep 30, 2020
 #1
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32 base a converted to base 10 is 3a + 2

23 base b converted to base 10 is 2b + 3

 

3a + 2 = 2b + 3

 

3a = 2b + 1

 

Guessing and checking we can easily get a = 5, b = 7.

 

5 + 7 = 12

 Sep 30, 2020
 #2
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Great job!

Guest Sep 30, 2020

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