The Exponential Diophantine Equation 2x+by=cz
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-3, 3 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-18
Country of Publication
Egypt
No. of Pages
3
Main Subjects
Medicine
Information Technology and Computer Science
Abstract EN
Let b and c be fixed coprime odd positive integers with min{b,c}>1.
In this paper, a classification of all positive integer solutions (x,y,z) of the equation 2x+by=cz is given.
Further, by an elementary approach, we prove that if c=b+2, then the equation has only the positive integer solution (x,y,z)=(1,1,1), except for (b,x,y,z)=(89,13,1,2) and (2r-1,r+2,2,2), where r is a positive integer with r≥2.
American Psychological Association (APA)
Yu, Yahui& Xiaoxue, Li. 2014. The Exponential Diophantine Equation 2x+by=cz. The Scientific World Journal،Vol. 2014, no. 2014, pp.1-3.
https://search.emarefa.net/detail/BIM-1049473
Modern Language Association (MLA)
Yu, Yahui& Xiaoxue, Li. The Exponential Diophantine Equation 2x+by=cz. The Scientific World Journal No. 2014 (2014), pp.1-3.
https://search.emarefa.net/detail/BIM-1049473
American Medical Association (AMA)
Yu, Yahui& Xiaoxue, Li. The Exponential Diophantine Equation 2x+by=cz. The Scientific World Journal. 2014. Vol. 2014, no. 2014, pp.1-3.
https://search.emarefa.net/detail/BIM-1049473
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1049473