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...
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| Format: | Article |
| Language: | English |
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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 |
| _version_ | 1825949622037643264 |
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| author | Yow, Kai Siong Sapar, Siti Hasana Atan, Kamel Ariffin |
| author_facet | Yow, Kai Siong Sapar, Siti Hasana Atan, Kamel Ariffin |
| author_sort | Yow, Kai Siong |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:47:23Z |
| format | Article |
| id | upm.eprints-40548 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:47:23Z |
| publishDate | 2013 |
| publisher | Universiti Putra Malaysia Press |
| record_format | dspace |
| spelling | upm.eprints-405482015-11-05T01:13:48Z http://psasir.upm.edu.my/id/eprint/40548/ On the diophantine equation x² + 4.7ᵇ = y²ʳ Yow, Kai Siong Sapar, Siti Hasana Atan, Kamel Ariffin 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. Universiti Putra Malaysia Press 2013 Article PeerReviewed application/pdf en 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 Yow, Kai Siong and Sapar, Siti Hasana and Atan, Kamel Ariffin (2013) On the diophantine equation x² + 4.7ᵇ = y²ʳ. Pertanika Journal of Science & Technology, 21 (2). pp. 443-458. ISSN 0128-7680; ESSN: 2231-8526 http://www.pertanika.upm.edu.my/Pertanika%20PAPERS/JST%20Vol.%2021%20%282%29%20Jul.%202013/12%20Page%20443-458.pdf |
| spellingShingle | Yow, Kai Siong Sapar, Siti Hasana Atan, Kamel Ariffin On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title | On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title_full | On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title_fullStr | On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title_full_unstemmed | On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title_short | On the diophantine equation x² + 4.7ᵇ = y²ʳ |
| title_sort | on the diophantine equation x² 4 7ᵇ y²ʳ |
| url | 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 |
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