The Diophantine Equation 8x+py=z2
Joint Authors
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-01-14
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
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).
American Psychological Association (APA)
Qi, Lan& Xiaoxue, Li. 2015. The Diophantine Equation 8x+py=z2. The Scientific World Journal،Vol. 2015, no. 2015, pp.1-3.
https://search.emarefa.net/detail/BIM-1078657
Modern Language Association (MLA)
Qi, Lan& Xiaoxue, Li. The Diophantine Equation 8x+py=z2. The Scientific World Journal No. 2015 (2015), pp.1-3.
https://search.emarefa.net/detail/BIM-1078657
American Medical Association (AMA)
Qi, Lan& Xiaoxue, Li. The Diophantine Equation 8x+py=z2. The Scientific World Journal. 2015. Vol. 2015, no. 2015, pp.1-3.
https://search.emarefa.net/detail/BIM-1078657
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1078657