Pell´s Equation
(2011) In Bachelor's Theses in Mathematical Sciences MATX01 20111Mathematics (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:
http://lup.lub.lu.se/studentpapers/record/2462740
 author
 Pang, Jenny
 supervisor

 Kjell Elfström ^{LU}
 organization
 course
 MATX01 20111
 year
 2011
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor's Theses in Mathematical Sciences
 report number
 LUNFMA40102011
 ISSN
 16546229
 other publication id
 2011:K2
 language
 English
 id
 2462740
 date added to LUP
 20141215 14:13:11
 date last changed
 20181011 16:23:18
@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 = {16546229}, language = {eng}, note = {Student Paper}, series = {Bachelor's Theses in Mathematical Sciences}, title = {Pell´s Equation}, year = {2011}, }