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/student-papers/record/2462740
- author
- Pang, Jenny
- supervisor
- organization
- course
- MATX01 20111
- year
- 2011
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses 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
- 2018-10-11 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 = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{Pell´s Equation}}, year = {{2011}}, }