Citation
Sihabudin, Nurul Amirah and Sapar, Siti Hasana and Mohamad Johari, Mohamad Aidil
(2017)
Simultaneous Pell equations x2 - my2 = 1 and y2 - pz2 = 1.
Malaysian Journal of Mathematical Sciences, 11 (spec. Apr.).
pp. 61-71.
ISSN 1823-8343; ESSN: 2289-750X
Abstract
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 equations x2 − 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/2 t ±1, yn, zn, y2n/4 t2) for yn odd and even respectively, where t ∈ N.
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Official URL or Download Paper: http://einspem.upm.edu.my/journal/fullpaper/vol11s...
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Additional Metadata
| Item Type: | Article |
|---|---|
| Divisions: | Faculty of Science Institute for Mathematical Research |
| Publisher: | Institute for Mathematical Research, Universiti Putra Malaysia |
| Notes: | Special issue: The 2nd International Conference and Workshop on Mathematical Analysis (ICWOMA 2016) |
| Keywords: | Simultaneous Pell equations; Pell equation and parity |
| Depositing User: | Nabilah Mustapa |
| Date Deposited: | 03 May 2017 04:29 |
| Last Modified: | 03 May 2017 04:34 |
| URI: | http://psasir.upm.edu.my/id/eprint/51916 |
| Statistic Details: | View Download Statistic |
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