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?
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