Bound on some Diophantine equation
Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the...
| Main Authors: | , , |
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| Format: | Article |
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Malaysian Mathematical Sciences Society
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100565/ |
| _version_ | 1848863356983705600 |
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| author | Amalulhair, N. H. Sapar, S. H. Johari, M. A. M. |
| author_facet | Amalulhair, N. H. Sapar, S. H. Johari, M. A. M. |
| author_sort | Amalulhair, N. H. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the equation for y = 2 and y > 2 with the bound on n < 15,000 and n < 11,000 respectively. |
| first_indexed | 2025-11-15T13:31:38Z |
| format | Article |
| id | upm-100565 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:31:38Z |
| publishDate | 2022 |
| publisher | Malaysian Mathematical Sciences Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1005652023-10-10T02:13:08Z http://psasir.upm.edu.my/id/eprint/100565/ Bound on some Diophantine equation Amalulhair, N. H. Sapar, S. H. Johari, M. A. M. Diophantine equation is known as a polynomial equation with two or more unknowns which only integral solutions are sought. This paper will concentrate on finding the least upper bound to the Diophantine equation x 2 + 2a 7 b = y n for 1 ≤ α ≤ 8 and found that there exists an integral solution to the equation for y = 2 and y > 2 with the bound on n < 15,000 and n < 11,000 respectively. Malaysian Mathematical Sciences Society 2022-07-29 Article PeerReviewed Amalulhair, N. H. and Sapar, S. H. and Johari, M. A. M. (2022) Bound on some Diophantine equation. Menemui Matematik (Discovering Mathematics), 44 (1). 28 - 34. ISSN 0126-9003 https://myjms.mohe.gov.my/index.php/dismath/article/view/18943 |
| spellingShingle | Amalulhair, N. H. Sapar, S. H. Johari, M. A. M. Bound on some Diophantine equation |
| title | Bound on some Diophantine equation |
| title_full | Bound on some Diophantine equation |
| title_fullStr | Bound on some Diophantine equation |
| title_full_unstemmed | Bound on some Diophantine equation |
| title_short | Bound on some Diophantine equation |
| title_sort | bound on some diophantine equation |
| url | http://psasir.upm.edu.my/id/eprint/100565/ http://psasir.upm.edu.my/id/eprint/100565/ |