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?
I'd do it like this
One solution is a=1 and b=1 (these are not real solutions yet but they work for this equation.
3(1+2t)-2(1+3t)=1 here I have added 6t and then taken it away again.
Now you can answer it.