Solvability of ternary equations of signature (3,3,2)

Date created: 
2014-08-11
Identifier: 
etd8509
Keywords: 
Diophantine equations
Generalized Fermat equations
Number theory
Ternary equations
Abstract: 

In this thesis we examine the primitive solvability of Diophantine equations of the form ax^3 + by^3 = cz^2. For square-free a, b, c, we identify various criteria necessary for the existence of primitive solutions, including a sufficient one. We also present a relatively efficient algorithm to determine whether this criterion is satisfied. Using the algorithm, we compute some data on the relative distribution of the occurrence of various obstructions to the existence of primitive solutions.

Document type: 
Thesis
Rights: 
Copyright remains with the author. The author granted permission for the file to be printed and for the text to be copied and pasted.
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Senior supervisor: 
Nils Bruin
Department: 
Science: Department of Mathematics
Thesis type: 
(Thesis) M.Sc.
Statistics: