On the Diophantine equation x2+p2k+1=4yn
It has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x, y. It is further proved that when n=3 and p...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202106107 |
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| _version_ | 1832553945284739072 |
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| author | S. Akhtar Arif Amal S. Al-Ali |
| author_facet | S. Akhtar Arif Amal S. Al-Ali |
| author_sort | S. Akhtar Arif |
| collection | DOAJ |
| description | It has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x, y. It is further proved that when n=3 and p=3a2±4, then it has a unique solution k=0, y=a2±1. |
| format | Article |
| id | doaj-art-67183dee59174e3588dd0c3944859580 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-67183dee59174e3588dd0c39448595802025-02-03T05:52:45ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-01311169569910.1155/S0161171202106107On the Diophantine equation x2+p2k+1=4ynS. Akhtar Arif0Amal S. Al-Ali1Department of Mathematics, Girls College of Education, P.O. Box 22171, Riyadh 11495, Saudi ArabiaDepartment of Mathematics, Girls College of Education, P.O. Box 56778, Riyadh 11564, Saudi ArabiaIt has been proved that if p is an odd prime, y>1, k≥0, n is an integer greater than or equal to 4, (n,3h)=1 where h is the class number of the field Q(−p), then the equation x2+p2k+1=4yn has exactly five families of solution in the positive integers x, y. It is further proved that when n=3 and p=3a2±4, then it has a unique solution k=0, y=a2±1.http://dx.doi.org/10.1155/S0161171202106107 |
| spellingShingle | S. Akhtar Arif Amal S. Al-Ali On the Diophantine equation x2+p2k+1=4yn International Journal of Mathematics and Mathematical Sciences |
| title | On the Diophantine equation x2+p2k+1=4yn |
| title_full | On the Diophantine equation x2+p2k+1=4yn |
| title_fullStr | On the Diophantine equation x2+p2k+1=4yn |
| title_full_unstemmed | On the Diophantine equation x2+p2k+1=4yn |
| title_short | On the Diophantine equation x2+p2k+1=4yn |
| title_sort | on the diophantine equation x2 p2k 1 4yn |
| url | http://dx.doi.org/10.1155/S0161171202106107 |
| work_keys_str_mv | AT sakhtararif onthediophantineequationx2p2k14yn AT amalsalali onthediophantineequationx2p2k14yn |