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Simultaneous pell equations x²-my² = 1 and y²-pz² = 1

Pell equation is a special type of Diophantine equations of the form x²−my²= 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions(x, y)to the Pell equation. This paper will discuss the integral solutions to the simultaneous...

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Main Authors: Sihabudin, Nurul Amirah, Safar, Siti Hasana, Johari, Mohamat Aidil
Format: Article
Language:English
Published: Institute for Mathematical Research, Universiti Putra Malaysia 2017
Online Access:http://psasir.upm.edu.my/id/eprint/63224/1/Simultaneous%20pell%20equations%20x%C2%B2-my%C2%B2%20%3D%201%20and%20y%C2%B2-pz%C2%B2%20%3D%201.pdf
http://psasir.upm.edu.my/id/eprint/63224/
http://einspem.upm.edu.my/journal
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spelling my.upm.eprints.632242019-04-15T08:33:30Z http://psasir.upm.edu.my/id/eprint/63224/ Simultaneous pell equations x²-my² = 1 and y²-pz² = 1 Sihabudin, Nurul Amirah Safar, Siti Hasana Johari, Mohamat Aidil Pell equation is a special type of Diophantine equations of the form x²−my²= 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions(x, y)to the Pell equation. This paper will discuss the integral solutions to the simultaneous Pell equationsx²−my²= 1 and y²−pz²= 1, where m is square free integer and p is odd prime. The solutions of these simultaneous equations are of the form of(x, y, z, m) = (yn²t±1, yn, zn, yn²t²±2t)and(y²n/²t±1, yn, zn, y²n/4t²±t) for yn odd and even respectively, where t ∈ N. Institute for Mathematical Research, Universiti Putra Malaysia 2017 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/63224/1/Simultaneous%20pell%20equations%20x%C2%B2-my%C2%B2%20%3D%201%20and%20y%C2%B2-pz%C2%B2%20%3D%201.pdf Sihabudin, Nurul Amirah and Safar, Siti Hasana and Johari, Mohamat Aidil (2017) Simultaneous pell equations x²-my² = 1 and y²-pz² = 1. Malaysian Journal of Mathematical Sciences, 11. 61 - 71. ISSN 1823-8343; ESSN: 2289-750X http://einspem.upm.edu.my/journal
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Pell equation is a special type of Diophantine equations of the form x²−my²= 1, where m is a positive non-square integer. Since m is not a perfect square, then there exist infinitely many integer solutions(x, y)to the Pell equation. This paper will discuss the integral solutions to the simultaneous Pell equationsx²−my²= 1 and y²−pz²= 1, where m is square free integer and p is odd prime. The solutions of these simultaneous equations are of the form of(x, y, z, m) = (yn²t±1, yn, zn, yn²t²±2t)and(y²n/²t±1, yn, zn, y²n/4t²±t) for yn odd and even respectively, where t ∈ N.
format Article
author Sihabudin, Nurul Amirah
Safar, Siti Hasana
Johari, Mohamat Aidil
spellingShingle Sihabudin, Nurul Amirah
Safar, Siti Hasana
Johari, Mohamat Aidil
Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
author_facet Sihabudin, Nurul Amirah
Safar, Siti Hasana
Johari, Mohamat Aidil
author_sort Sihabudin, Nurul Amirah
title Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
title_short Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
title_full Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
title_fullStr Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
title_full_unstemmed Simultaneous pell equations x²-my² = 1 and y²-pz² = 1
title_sort simultaneous pell equations x²-my² = 1 and y²-pz² = 1
publisher Institute for Mathematical Research, Universiti Putra Malaysia
publishDate 2017
url http://psasir.upm.edu.my/id/eprint/63224/1/Simultaneous%20pell%20equations%20x%C2%B2-my%C2%B2%20%3D%201%20and%20y%C2%B2-pz%C2%B2%20%3D%201.pdf
http://psasir.upm.edu.my/id/eprint/63224/
http://einspem.upm.edu.my/journal
_version_ 1643837750812606464
score 13.211869

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