MINOR CONTRIBUTION UPTO THIS POINT
1) VJ's Golden Lemma
It gives systematic way to expand power of multinomial which is essential / needed to compute n'th root or power of any number efficiently in one line.
2) VJ's Cross divisibility Test / Universal divisibility test
Single formula for deriving devisibility test for any number..
3) Two step Method
4) Elimination- Retension Method
By using this method one can do square-cube or higher power of any number in structural manner.
5) VJ's Matrix Method
One line method for computing n'th root & root of any algebraic equation.. Efficient, systematic & elegant than Newton's method.