The Diophantine equation $aX^{4} - bY^{2} = 1$
Number Theory
2009-03-11 v1
Abstract
As an application of the method of Thue-Siegel, we will resolve a conjecture of Walsh to the effect that the Diophantine equation , for fixed positive integers and , possesses at most two solutions in positive integers and . Since there are infinitely many pairs for which two such solutions exist, this result is sharp.
Keywords
Cite
@article{arxiv.0903.1742,
title = {The Diophantine equation $aX^{4} - bY^{2} = 1$},
author = {Shabnam Akhtari},
journal= {arXiv preprint arXiv:0903.1742},
year = {2009}
}
Comments
20 pages, To appear in Journal fur die Reine und Angewandte Mathematik (Crelle's Journal)