Although a proof of its insolubility was first attempted by Paolo Ruffini, FTP, what type of equation has no solutions in the form of radicals, as proven by Nils Abel and Evariste Galois?
It has a general solution in terms of Jacobi theta functions, and Hermite showed how it could be done by reducing it to Bring form. Felix Klein found hypergeometric solutions by reducing it via a Tschirnhausen transformation and solving the related icosahedral equation, and in general, an irreducible one can be associated with a symmetric, metacyclic, dihedral, alternating, or cyclic group. Although a proof of its insolubility was first attempted by Paolo Ruffini, FTP, what type of equation has no solutions in the form of radicals, as proven by Nils Abel and Evariste Galois?
It has a general solution in terms of Jacobi theta functions, and Hermite showed how it could be done by reducing it to Bring form.
{Quintic} (or: the equation of {fifth degree} or logical equivalents)