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On the diophantine equation px+5y=z2 |
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| รหัสดีโอไอ | |
| Creator | I-lada Cheenchan |
| Title | On the diophantine equation px+5y=z2 |
| Publisher | Sakon Nakhon Rajabhat University |
| Publication Year | 2559 |
| Journal Title | SNRU Journal of Science and Technology |
| Journal Vol. | 8 |
| Journal No. | 1 |
| Page no. | 146-148 |
| Keyword | Exponential Diophantine equation, Integer solutions, Congruent |
| ISSN | 1906-5965 |
| Abstract | The aim of this work is to show that the Diophantine equations p z x y ? ? 5 2 where p is prime numberand p satisfies ; case 1 : p ?1 (mod 4) or case 2 : p ? 3 (mod 4) and p ? 2 (mod 5) or case 3 :p ? 3 (mod 4) and p ? 3 (mod 5) , has no non-negative integer solution. In addition, the Diophantineequations p z x y ? ? 5 2 have some non-negative integer solutions ( p, x, y, z ) if p ? 3(mod 4) andp ? 1(mod 5) , such as (11 ,1 ,2 , 6) , (11 , 1 ,1 ,4) , (31 ,1 ,1 ,6) , (71 ,1 ,3 ,4) , (131 ,1 ,3 ,16) and (191 ,1 ,1 ,14),etc. Moreover, if p ? 3(mod 4) and p ? 4(mod 5), such as (19 ,1 ,3 ,12) , (139 , 1 ,1 ,12) and (199 , 1 ,3 ,18). |
