On The Diophantine Equation:Jesmanowicz Conjecture And Selected Special Cases
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Date
2020-11
Authors
Abdulrahman Hamed Ahmed Balfaqih
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Publisher
Universiti Sains Malaysia
Abstract
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.
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On The Diophantine Equation , Jesmanowicz Conjecture And Selected Special Cases