On the cubic Pell equation over finite fields

DOI10.2989/16073606.2022.2144531arXiv2203.05290OpenAlexW4318820012MaRDI QIDQ6081485

Simone Dutto, Nadir Murru

Publication date: 5 October 2023

Published in: Quaestiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.05290

zbMATH Keywords

finite fieldsPell equationcubic Pell equation

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Cubic and quartic Diophantine equations (11D25)

Related Items (1)

DLP-based cryptosystems with Pell cubics

Cites Work

• Unnamed Item
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• Solving the Pell equation
• A note on cyclic groups, finite fields, and the discrete logarithm problem
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• Explicit formula for the solution of simultaneous Pell equations 𝑥²-(𝑎²-1)𝑦²=1, 𝑦²-𝑏𝑧²=1
• Units and Periodic Jacobi-Perron Algorithms in Real Algebraic Number Fields of Degree 3
• Strong arithmetic properties of the integral solutions of X³ + DY³ + D²Z³ - 3DXYZ = 1, where D = M³ ± 1, M ∈ ℤ*
• Fundamental units from the perperiod of a generalized Jacobi-Perron algorithm.
• Chebyshev polynomials and Pell equations over finite fields
• On the solvability of the simultaneous Pell equations x2 − ay2 = 1 and y2 − bz2 = v12
• A Remark on Solutions of the Pell Equation
• Pell's equation

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