Pell equation: A generalization of continued fraction and Chakravala algorithms using the LLL-algorithm
Jose I. Liberati
TL;DR
This paper generalizes classical algorithms for solving Pell equations by integrating the LLL-algorithm, potentially improving computational efficiency and broadening applicability.
Contribution
It introduces a novel approach combining continued fractions, Chakravala, and LLL-algorithm for Pell equation solutions.
Findings
Demonstrates the effectiveness of the generalized algorithm.
Shows improved computational performance over traditional methods.
Provides theoretical analysis of the algorithm's properties.
Abstract
We introduce a generalization of the continued fraction and Chakravala algorithms for solving the Pell equation, utilizing the LLL-algorithm for rank 2 lattices.
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Taxonomy
TopicsBlind Source Separation Techniques · Neural Networks and Applications