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Showing 1 to 6 of 6 for “"Linear forms in logarithms"”.
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Linear Forms in Logarithms and Fibonacci Numbers
The main work included in these pages is from a paper co-written by myself and my brother, Simon Earp-Lynch, under the supervision of Omar Kihel, pertaining to Diophantine triples of Fibonacci numbers. To go along with this will be introductory material not included in said paper which establishes …
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Linear Forms in Logarithms and Integer Points on Genus-two Curves
We consider a linear form with algebraic coefficients, evaluated at points on the analytic Jacobian of a genus-two curve whose projective coordinates are algebraic. Previous results on the existence of a lower bound of a particular shape are made explicit. We study various properties of Jacobians …
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On the Extendibility of a D(4)-Pair of Pell Numbers
A Diophantine m-tuple with property D(ℓ) is a set of m integers such that the product of any two integers plus ℓ results in a perfect square. This thesis establishes that a particular family of D(4) pairs of Pell numbers can be extended to a D(4) triple by exactly one Pell number. A similar result …
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Thue equations and related topics
Using a classical result of Thue, we give an upper bound for the number of solutions to a family of quartic Thue equations. We also give an upper bound upon the number of solutions to a family of quartic Thue inequalities. Using the Thue-Siegel principle and the theory of linear forms in …
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Nonexistence of Solutions to Certain Families of Diophantine Equations
<p>In this work, I examine specific families of Diophantine equations and prove that they have no solutions in positive integers. The proofs use a combination of classical elementary arguments and powerful tools such as Diophantine approximations, Lehmer numbers, the modular approach, and earlier …