On the Diophantine equation x2+p2k+1=4yn
It has been proved that if p is an odd prime, y > 1, k0, 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...
Saved in:
| Published in | International journal of mathematics and mathematical sciences Vol. 31; no. 11; pp. 695 - 699 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Wiley
01.01.2002
|
| Online Access | Get full text |
Cover
Loading…
| Summary: | It has been proved that if p is an odd prime, y > 1, k0, 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=3a24, then it has a unique solution k=0, y=a21. |
|---|---|
| Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
| ISSN: | 0161-1712 1687-0425 |
| DOI: | 10.1155/S0161171202106107 |