Citation
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
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 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.
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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: | Mr. Sazali Mohamad |
| Date Deposited: | 15 Apr 2019 08:32 |
| Last Modified: | 15 Apr 2019 08:33 |
| URI: | http://psasir.upm.edu.my/id/eprint/63224 |
| Statistic Details: | View Download Statistic |
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