Pell's equation without irrational numbers
N. J. Wildberger
TL;DR
This paper presents a straightforward method for solving Pell's equation without using continued fractions or irrational numbers, linking the solution process to the Stern Brocot tree structure.
Contribution
Introduces a novel approach to solving Pell's equation that avoids traditional irrational number methods and connects to the Stern Brocot tree.
Findings
Solution method is simpler and more accessible.
Establishes a connection between Pell's equation and Stern Brocot tree.
Potential for improved computational efficiency.
Abstract
We solve Pell's equation in a simple way without continued fractions or irrational numbers, and relate the algorithm to the Stern Brocot tree.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical and Theoretical Analysis · Polynomial and algebraic computation