On the diophantine equation x² + 4.7ᵇ = y²ʳ
This paper investigates and determines the solutions for the Diophantine equation x²+ 4.7ᵇ= y²ͬ, where x, y, bare all positive intergers and r> 1. By substituting the values of rand b respectively, generators of x and yͬ can be determined and classified into different categories. Then, by using g...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universiti Putra Malaysia Press
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/40548/1/38.%20On%20the%20diophantine%20equation%20x%C2%B2%20%2B%204.7%E1%B5%87%20%3D%20y%C2%B2%CA%B3.pdf |
| Summary: | This paper investigates and determines the solutions for the Diophantine equation x²+ 4.7ᵇ= y²ͬ, where x, y, bare all positive intergers and r> 1. By substituting the values of rand b respectively, generators of x and yͬ can be determined and classified into different categories. Then, by using geometric progression method, a general formula for each category can be obtained. The necessary conditions to obtain the integral solutions of x and y are also investigated. |
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