Advanced

Pell´s Equation

Pang, Jenny (2011) In Bachelor's Thesis in Mathematical Sciences MATX01 20111
Mathematics (Faculty of Sciences)
Abstract
Pell`s equation has been studied since ancient times. The interest in
Pell`s equation began as many natural questions that one might ask about
integers lead to a quadratic equation in two variables, which in turn can be cast as a Pell`s equation. This thesis covers the development from the first contribution of the Indian mathematician Brahmagupta to an alternative proof of existence of solutions given by Dirichlet.
We begin by explaining the fundamentals of continued fractions. We
then present two proofs of existence of solutions to Pell`s equation. After that we consider some examples. We finish with a historical note.
The curious reader can find a description of the Indians' methods in the
appendix.
Please use this url to cite or link to this publication:
author
Pang, Jenny
supervisor
organization
course
MATX01 20111
year
type
M2 - Bachelor Degree
subject
publication/series
Bachelor's Thesis in Mathematical Sciences
report number
LUNFMA-4010-2011
ISSN
1654-6229
other publication id
2011:K2
language
English
id
2462740
date added to LUP
2014-12-15 14:13:11
date last changed
2014-12-15 14:13:11
@misc{2462740,
  abstract     = {Pell`s equation has been studied since ancient times. The interest in
Pell`s equation began as many natural questions that one might ask about
integers lead to a quadratic equation in two variables, which in turn can be cast as a Pell`s equation. This thesis covers the development from the first contribution of the Indian mathematician Brahmagupta to an alternative proof of existence of solutions given by Dirichlet.
We begin by explaining the fundamentals of continued fractions. We
then present two proofs of existence of solutions to Pell`s equation. After that we consider some examples. We finish with a historical note.
The curious reader can find a description of the Indians' methods in the
appendix.},
  author       = {Pang, Jenny},
  issn         = {1654-6229},
  language     = {eng},
  note         = {Student Paper},
  series       = {Bachelor's Thesis in Mathematical Sciences},
  title        = {Pell´s Equation},
  year         = {2011},
}