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The degree of the polynomial

Edward Waring (1734-1793), an English mathematician, searched for the correlations between the degrees of the resolvent polynomials of a polynomial. A polynomial of first degree is its own resolvent, a polynomial of second degree has a linear polynomial as a resolvent, a polynomial of third degree is first transformed into one of sixth and then into one of second, and finally into a linear one. All people managed to do with the quintic was 5-120-30-6, but 6>5, so the last resolvent was more complex than the starting polynomial.

Leo Liberti
Thu Feb 26 17:04:11 CET 1998