The Diophantine Equation 8x+py=z2
| Autor: | Lan Qi, Xiaoxue Li |
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| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | The Scientific World Journal, Vol 2015 (2015) |
| Druh dokumentu: | article |
| ISSN: | 2356-6140 1537-744X |
| DOI: | 10.1155/2015/306590 |
| Popis: | Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod 8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod 8), then the equation has only the solutions (p,x,y,z)=(2q-1,(1/3)(q+2),2,2q+1), where q is an odd prime with q≡1(mod 3); (iii) if p≡1(mod 8) and p≠17, then the equation has at most two positive integer solutions (x,y,z). |
| Databáze: | Directory of Open Access Journals |
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