Circularity in finite fields and solutions of the equations xm + ym − zm = 1

Wen Fong Ke; Hubert Kiechle

doi:10.1016/j.ffa.2024.102467

Circularity in finite fields and solutions of the equations x^m + y^m − z^m = 1

Wen Fong Ke, Hubert Kiechle

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only on the exponent and the characteristic of the field, holds. This formula improves the one given by the authors in an earlier paper.

Original language	English
Article number	102467
Journal	Finite Fields and their Applications
Volume	98
DOIs	https://doi.org/10.1016/j.ffa.2024.102467
Publication status	Published - 2024 Sept

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2024.102467

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abstract = "An explicit formula for the number of solutions of the equation in the title is given when a certain condition, depending only on the exponent and the characteristic of the field, holds. This formula improves the one given by the authors in an earlier paper.",

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Circularity in finite fields and solutions of the equations xm + ym − zm = 1

Abstract

All Science Journal Classification (ASJC) codes

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Circularity in finite fields and solutions of the equations x^m + y^m − z^m = 1