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The work of Vandermonde and Gauss

Vandermonde proposed in 1770 that the key to solving a general polynomial equation
was represented by the roots of the equation tex2html_wrap_inline308. Gauss has the undoubted credit for having laid the first stone in the path that Galois successively followed. He showed that the roots of the polynomial equation tex2html_wrap_inline310 where p is prime are rational functions of the roots of a sequence of equations tex2html_wrap_inline314 where the coefficients of tex2html_wrap_inline316 are rational expressions of the roots of tex2html_wrap_inline318 and the degrees of the polynomials in the sequence are the all the prime numbers in the factorization of p-1.

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