PROBLEM: for instance to rationalize

find which makes a


It is easily shown, that the complete problem can be solved if it can be solved for and .

0) Find ; new intermediate radicals are

1) Select the prime number p which is a factor of L, rewrite the radicals as , consider the inner roots as new radicands

2) - To get rewrite where the are replaced by in .

- To get rewrite where the are replaced by in .

  1. Solve for the resulting expression (1 + S1a) or (1 + S1b), the new L for the remaining radicals will be L/p

  2. Repeat for the result of (3) from (1) until no radicals remain

The 'damage' done by the 'factoring' in (2) is simple to repair.

THE I N T U I T I O N I WAS UNABLE TO PROVE UP TO NOW IS

,

For instance



I would like to know if the intuition is right ( I checked it for discrete cases as far as 1 gibabyte swap, using the computer algebra program MuPAD, allowed )

and some HINTS how to prove it.

Proving for sqareroots is easy:

If it's true for and then in the product is substituted with the x of the expanded product are replace by

and the expanded product can be written , where R,S are polynomials. Take the produkt both nonPoly values

and you again get a plolynomial, and in the product each factor f is substituted by the two factors .