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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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2017
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| 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 |
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| author | Sihabudin, Nurul Amirah Safar, Siti Hasana Johari, Mohamat Aidil |
| author_facet | Sihabudin, Nurul Amirah Safar, Siti Hasana Johari, Mohamat Aidil |
| author_sort | Sihabudin, Nurul Amirah |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T09:44:01Z |
| format | Article |
| id | upm.eprints-63224 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T09:44:01Z |
| publishDate | 2017 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Sihabudin, Nurul Amirah Safar, Siti Hasana Johari, Mohamat Aidil Simultaneous pell equations x²-my² = 1 and y²-pz² = 1 |
| title | 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_short | Simultaneous pell equations x²-my² = 1 and y²-pz² = 1 |
| title_sort | simultaneous pell equations x² my² 1 and y² pz² 1 |
| 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 |
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