Citation
Bakar, H. S. and Sapar, S. H. and Johari, M. A. M.
(2019)
On the Diophantine Equation 5 x + p mn y = z 2.
Malaysian Journal of Mathematical Sciences, 13 (spec.).
pp. 41-50.
ISSN 1823-8343; ESSN: 2289-750X
Abstract
Diophantine equation is a polynomial equation with two or more unknowns for which only integral solutions are sought. This paper concentrates on finding the integral solutions to the Diophantine equation 5 x + p mn y = z 2 where p > 5 a prime number and y = 1, 2. The positive integral solutions to the equation are (x, m, n, y, z) = (2r, t, pt k 2 ± 2k5 r , 1, pt k ± 5 r ) and 2r, 2t, 5 2r−α − 5 α 2p t , 2, 5 2r−α + 5α 2 for k, r, t ∈ N where 0 ≤ α < r.
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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 |
| Keywords: | Diophantine; Physic; Theory |
| Depositing User: | Ms. Zaimah Saiful Yazan |
| Date Deposited: | 14 May 2024 07:13 |
| Last Modified: | 14 May 2024 07:13 |
| URI: | http://psasir.upm.edu.my/id/eprint/81535 |
| Statistic Details: | View Download Statistic |
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