Higher Descent on Pell Conics I. From Legendre to Selmer

Abstract

This article deals with the history of certain aspects of the Pell equation X${}^2$ - D y${}^2$ = 4. We briefly discuss explicit units, and then study the history of Legendre's equations ax${}^2$ - b y${}^2$ = 4 with ab=D.

19 pages, 2 figures

References in corpus (4)

• Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields
• Multi-variable Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields
• Higher Descent on Pell Conics III. The First 2-Descent
• Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities

Cited by in corpus (4)

• Conics - a Poor Man's Elliptic Curves
• On the Liouville function at polynomial arguments
• Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities
• Approximation diophantienne et distribution locale sur une surface torique II