On the Diophantine equation x2+2k=yn
By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding the solutions of this equation has been put forward and proved to be true for a large class of values of k and n.
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| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171297000409 |
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| _version_ | 1832563087162474496 |
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| author | S. Akhtar Arif Fadwa S. Abu Muriefah |
| author_facet | S. Akhtar Arif Fadwa S. Abu Muriefah |
| author_sort | S. Akhtar Arif |
| collection | DOAJ |
| description | By factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various
theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding
the solutions of this equation has been put forward and proved to be true for a large class of values of k
and n. |
| format | Article |
| id | doaj-art-6ce223ebc4484c63942722283a0c0366 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6ce223ebc4484c63942722283a0c03662025-02-03T01:20:56ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-0120229930410.1155/S0161171297000409On the Diophantine equation x2+2k=ynS. Akhtar Arif0Fadwa S. Abu Muriefah1Department of Mathematics, Girls College of Education, Al-Riyadh, Saudi ArabiaDepartment of Mathematics, Girls College of Education, Al-Riyadh, Saudi ArabiaBy factorizing the equation x2+2k=yn, n≥3, k-even, in the field Q(i), various theorems regarding the solutions of this equation in rational integers are proved. A conjecture regarding the solutions of this equation has been put forward and proved to be true for a large class of values of k and n.http://dx.doi.org/10.1155/S0161171297000409 |
| spellingShingle | S. Akhtar Arif Fadwa S. Abu Muriefah On the Diophantine equation x2+2k=yn International Journal of Mathematics and Mathematical Sciences |
| title | On the Diophantine equation x2+2k=yn |
| title_full | On the Diophantine equation x2+2k=yn |
| title_fullStr | On the Diophantine equation x2+2k=yn |
| title_full_unstemmed | On the Diophantine equation x2+2k=yn |
| title_short | On the Diophantine equation x2+2k=yn |
| title_sort | on the diophantine equation x2 2k yn |
| url | http://dx.doi.org/10.1155/S0161171297000409 |
| work_keys_str_mv | AT sakhtararif onthediophantineequationx22kyn AT fadwasabumuriefah onthediophantineequationx22kyn |