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Abel's impossibility theorem states that the roots of a general polynomial (of degree 5 or higher) cannot be written using arithmetic operations and radicals. Radicals are solutions of a specific ...

Given an irreducible solvable equation $P(x)=0$ of prime degree $p>2$ with rational coefficients and $\zeta^p=1$, define the usual Lagrange resolvents of the roots $x_i$ as, $$R_n = \big(x_1+x_2\...