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arXiv · 2307.05586

Circularity in Finite Fields and Solutions of the Equations $\boldsymbol{x^{m}+y^{m}-z^{m}=1}$

Wen-Fong Ke·Hubert Kiechle
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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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Wen-Fong Ke, Hubert Kiechle. 2023-07-13. Circularity in Finite Fields and Solutions of the Equations $\boldsymbol{x^{m}+y^{m}-z^{m}=1}$. https://doi.org/10.1016/j.ffa.2024.102467

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