On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases
In 1956, Jes´manowicz conjectured that for any primitive Pythagorean triple (a, b, c) with the Diophantine equation a2 + b2 = c2 and any positive integer k, the only solution of equation (ak)x +(bk)y = (ck)z, in positive integers, is (x, y, z) = (2, 2, 2). It is a famous unsolved conjecture on Pytha...
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| Format: | Thesis |
| Language: | English |
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2020
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| Online Access: | http://eprints.usm.my/52545/ http://eprints.usm.my/52545/1/Pages%20from%20ABDULRAHMAN%20HAMED%20AHMED%20BALFAQIH%20-%20TESIS.pdf |
| _version_ | 1848882285645922304 |
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| author | Ahmed Balfaqih, Abdulrahman Hamed |
| author_facet | Ahmed Balfaqih, Abdulrahman Hamed |
| author_sort | Ahmed Balfaqih, Abdulrahman Hamed |
| building | USM Institutional Repository |
| collection | Online Access |
| description | In 1956, Jes´manowicz conjectured that for any primitive Pythagorean triple (a, b, c) with the Diophantine equation a2 + b2 = c2 and any positive integer k, the only solution of equation (ak)x +(bk)y = (ck)z, in positive integers, is (x, y, z) = (2, 2, 2). It is a famous unsolved conjecture on Pythagorean triples and exponential Diophantine equations, and generally it has not been solved yet. In this thesis, there are six chapters all together. The first chapter is on introduction of the thesis. Chapter 2 represents preliminaries and literature review. |
| first_indexed | 2025-11-15T18:32:29Z |
| format | Thesis |
| id | usm-52545 |
| institution | Universiti Sains Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T18:32:29Z |
| publishDate | 2020 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | usm-525452022-05-20T01:59:00Z http://eprints.usm.my/52545/ On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases Ahmed Balfaqih, Abdulrahman Hamed QA1 Mathematics (General) In 1956, Jes´manowicz conjectured that for any primitive Pythagorean triple (a, b, c) with the Diophantine equation a2 + b2 = c2 and any positive integer k, the only solution of equation (ak)x +(bk)y = (ck)z, in positive integers, is (x, y, z) = (2, 2, 2). It is a famous unsolved conjecture on Pythagorean triples and exponential Diophantine equations, and generally it has not been solved yet. In this thesis, there are six chapters all together. The first chapter is on introduction of the thesis. Chapter 2 represents preliminaries and literature review. 2020-11 Thesis NonPeerReviewed application/pdf en http://eprints.usm.my/52545/1/Pages%20from%20ABDULRAHMAN%20HAMED%20AHMED%20BALFAQIH%20-%20TESIS.pdf Ahmed Balfaqih, Abdulrahman Hamed (2020) On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases. PhD thesis, Universiti Sains Malaysia. |
| spellingShingle | QA1 Mathematics (General) Ahmed Balfaqih, Abdulrahman Hamed On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title | On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_full | On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_fullStr | On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_full_unstemmed | On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_short | On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_sort | on the diophantine equation:jesmanowicz conjecture and selected special cases |
| topic | QA1 Mathematics (General) |
| url | http://eprints.usm.my/52545/ http://eprints.usm.my/52545/1/Pages%20from%20ABDULRAHMAN%20HAMED%20AHMED%20BALFAQIH%20-%20TESIS.pdf |