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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my-usm-ep.525452022-05-20T01:59:00Z On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases 2020-11 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 http://eprints.usm.my/52545/ http://eprints.usm.my/52545/1/Pages%20from%20ABDULRAHMAN%20HAMED%20AHMED%20BALFAQIH%20-%20TESIS.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik |
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Universiti Sains Malaysia |
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USM Institutional Repository |
| language |
English |
| topic |
QA1 Mathematics (General) |
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QA1 Mathematics (General) Ahmed Balfaqih, Abdulrahman Hamed On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| 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. |
| format |
Thesis |
| qualification_name |
Doctor of Philosophy (PhD.) |
| qualification_level |
Doctorate |
| author |
Ahmed Balfaqih, Abdulrahman Hamed |
| author_facet |
Ahmed Balfaqih, Abdulrahman Hamed |
| author_sort |
Ahmed Balfaqih, Abdulrahman Hamed |
| title |
On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases |
| title_short |
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_sort |
on the diophantine equation:jesmanowicz conjecture and selected special cases |
| granting_institution |
Universiti Sains Malaysia |
| granting_department |
Pusat Pengajian Sains Matematik |
| publishDate |
2020 |
| url |
http://eprints.usm.my/52545/1/Pages%20from%20ABDULRAHMAN%20HAMED%20AHMED%20BALFAQIH%20-%20TESIS.pdf |
| _version_ |
1747822189058457600 |