Higher Descent on Pell Conics II. Two Centuries of Missed Opportunities

Abstract

We discuss the history of attempts to solve the Pell equation using certain auxiliary equations that correspond, in modern terminology, to a second 2-descent.

arXiv comment11 pages

References in corpus (5)

• 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 I. From Legendre to Selmer
• Higher Descent on Pell Conics III. The First 2-Descent
• Method of Hidden Parameters and Pell's Equation

Cited by in corpus (2)

• Conics - a Poor Man's Elliptic Curves
• Higher Descent on Pell Conics I. From Legendre to Selmer