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Are fifth-degree equations over GF(5m) solvable by radicals?

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Abstract

Irreducible quintics over finite fields are solvable in closed form with the possible exception of characteristic 5 fields. It is shown that this is equally true for fifth-degree equations overGF(5m). The result follows from an Artin-Schreier theorem that yields explicit expressions for the roots ofx 5−x−a. In addition to what at present is known for all other finite fields, any quintic can be solved in closed form.

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Authors and Affiliations

  1. Dipartimento di Elettronica, Politecnico di Torino, I-10129, Torino, Italy

    Michele Elia

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  1. Michele Elia
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This work was financially supported in part by Politecnico di Torino from grant No. POLI4169-87-Cap11205

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Elia, M. Are fifth-degree equations over GF(5m) solvable by radicals?. AAECC 7, 27–40 (1996). https://doi.org/10.1007/BF01613614

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  • DOI: https://doi.org/10.1007/BF01613614

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