I have read this question, and learn that mostly we use strong mathematical induction while more than one base case is needed
Then, I wonder for the same proposition, whether we always require more base cases using strong basic induction than common(weak) mathematical induction or not?
Not really. That question needed more base cases by its nature. Most strong induction and weak induction usually only require one base case.
The real difference between strong and we is that strong will require the case to be true for all cases less than the one we are doing induction on, whereas weak induction only requires we know the induction case is true.
Therefore strong induction can rely on multiple earlier values. Thus if the statement is of the nature that it combines earlier values strong induction is a good choice.
Actually in the case we could just as easily used weak induction but it'it'd require the same number of base cases.
