Method of Hidden Parameters and Pell's Equation
S.N. Arteha
TL;DR
This paper introduces a new 'method of hidden parameters' to simplify solving Pell's equation, deriving formulas linking solutions across different cases and providing a parametric representation of solutions.
Contribution
It develops a novel 'method of hidden parameters' that reduces calculation steps and offers new formulas and parametric solutions for Pell's equation.
Findings
Derived formulas linking solutions of Pell's equation for different parameters
Introduced a new parametric representation of solutions
Reduced the number of calculation steps for solving Pell's equation
Abstract
Using the representation of numbers, the methods of decreasing the number of calculation steps for Pell's equation are developed. The formulae relating the natural solution x0 of Pell's equation for A0 with the infinite number of minimal natural solutions xi for other Ai are obtained for various cases. The parametric representation of Pell's equation solutions are obtained with the help of new "method of hidden parameters".
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsNeural Networks and Applications