The Exponential Diophantine Equation 2x+by=cz
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,...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/401816 |
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| Summary: | 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. |
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| ISSN: | 2356-6140 1537-744X |