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?
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