Solving the Quintic: A New Approach to Bring's Transformation

Jorge Franco

doi:10.20944/preprints202112.0272.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 15 December 2021 / Approved: 16 December 2021 / Online: 16 December 2021 (12:26:29 CET)

Applying a procedure similar to that of E.S. Bring, by using a 4^th degree Tschirnhaus transformation, it was possible to transform the Bring-Jerrard normal quintic (BJQ) equation into a De Moivre form (DMQ), so that it could be solved by radicals. The general solution by radicals of the De Moivre equations of any degree is presented. By the same procedure the BJSx (normal sextic) equation was taken to another one without the 2^nd, 4^th and 6^th terms which was transformed into a cubic (solvable) equation. By applying a 6^th degree Tschirnhaus transformation to the BJSp (normal septic) equation its binormal (without the 2^nd, 3^rd, 4^th and 5^th terms) form was obtained.

Solution of the Quintic by Radicals; Solution of the Sextic by Radicals; Solution of the De Moivre Equation of any degree by Radicals; Eliminating Four Terms at once from the Septic.

Computer Science and Mathematics, Algebra and Number Theory

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Solving the Quintic: A New Approach to Bring's Transformation

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