On an elementary method for solving $Ax^4-By^2=1$
Number Theory
2026-03-09 v1
Abstract
A new method for solving quartic equations due to Luo and Lin is investigated both computationally and theoretically. As a result, a completely straightforward elementary method is given for solving Bumby's equation , along with a conjecture, which if resolved, would enable a similar proof for a possibly infinite family of similar equations.
Keywords
Cite
@article{arxiv.2603.05809,
title = {On an elementary method for solving $Ax^4-By^2=1$},
author = {P. G. Walsh},
journal= {arXiv preprint arXiv:2603.05809},
year = {2026}
}