Home Page for John Robertson

Links to my Pell equation and binary quadratic equation pages

Solving the generalized Pell equation - PDF File
Fundamental Solutions to Generalized Pell Equations - PDF File
Diagram of Fundamental Solutions to Generalized Pell Equations - PDF File
Fundamental Solutions to Generalized Pell Equations--Long Version - PDF File
Solving the equation ax^2 + bxy + cy^2 + dx + ey + f = 0 - PDF File
Matthews' method for ax^2 + bxy + cy^2 = N - PDF File
Computing in Quadratic Orders - PDF File
Linear Recurrences for Pell Equations - PDF File
A Fast Algorithm for Computing the Regulator of an Order of a Real Quadratic Field-PDF File
Ambiguous Forms and Ideals in Quadratic Orders
Using Shanks' Baby-Step Giant-Step Method to Solve the Generalized Pell Equation x^2 - Dy^2 = N
Best Approximations to sqrt(D)

Keith Matthews pages related to Pell equations

Solving generalized Pell equations
Solving binary quadratic form equations
Certain Pell equations
CALC - system for number theory (includes ``patz'' for Pell equations and ``binform'' for BQF equations)
BC programs (includes Thue)

Talk given at 2009 Joint Mathematics Meetings

Nearest Square Continued Fractions, and Related Topics (talk) (talk with notes)

Other continued fraction and Pell equation pages

H. W. Lenstra Jr on solving Pell equations
Record-holder solutions of Pell equations
Continued fractions pages at Number Theory Web
Generalized Pell equation pages at Number Theory Web
Continued fraction page at World of Mathematics
Pell equation page at World of Mathematics
MacTutor page on Pell equation
Mathematical Excalibur - see 6-3 and 7-1 for Pell equation

The continued fraction expansions of sqrt(D) and (1+sqrt(D))/2

Question on subject cf expansions - text file
Proof that L4=3, L1=7 is not possible - PDF File

Comments on other papers

Podsypanin's paper on the length of the period of a quadratic irrational
Answers to Shirali's questions on sums of quadratic residues

Magic squares

Magic squares of squares
No 3x3 binary palindrome magic squares
Some comments on 4x4 magic squares
Searching for 4x4 magic squares
Christian Boyer's magic squares page

Other pages of interest

Number Theory Web
Keith Matthews home page
Richard Mollin home page
Robin Chapman home page
James Mc Laughlin home page
Mathematical Association of America
American Mathematical Society
American Mathematics Competitions
Mathematical Sciences Research Institute (MSRI)
Clay Mathematics Institute prize problems
Dave Rusin's mathematical atlas
Kevin Brown's essays on number theory
World of Mathematics Number Theory page

Sailing Links

Links to sailing sites


John P. Robertson

I live in South Florida and work as an actuary.

My interests include mathematics, especially curves of genus zero (Pell's equations and related topics), movies, and small boat sailing.

Last Modified January 17, 2009