When some number a^{2} is written in base b, the result is 144_{b} . a and b also happen to be integer side lengths of a right triangle. If a and b are both less than 20, find the sum of all possible values of a.
When some number a^{2} is written in base b, the result is 144_{b} . a and b also happen to be integer side lengths of a right triangle. If a and b are both less than 20, find the sum of all possible values of a.