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?
+118609 I'd do it like this
2+3a=3+2b
3a-2b=1
One solution is a=1 and b=1 (these are not real solutions yet but they work for this equation.
3(1)-2(1)=1
3(1+2t)-2(1+3t)=1 here I have added 6t and then taken it away again.
| t | 1 | 2 | 3 | 4 |
| a=1+2t | 3 | 5 | 7 | 9 |
| b=1+3t | 4 | 7 | 10 | 13 |
Now you can answer it.
