Some solutions of diophantine equation x3+y3=pk z3

Diophantine equation is an algebraic equation in two or more variables in which solutions to it are from some predetermined classes and it is one of the oldest branches of number theory. They are studied and investigated to determine the values of the variables that satisfy the equation. This activi...

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Main Author:	See, Kok Leong
Format:	Thesis
Language:	English
Published:	2011
Subjects:	Diophantine analysis
Online Access:	http://psasir.upm.edu.my/id/eprint/66457/1/IPM%202011%2022%20IR.pdf
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id	my-upm-ir.66457
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spelling	my-upm-ir.664572019-01-23T23:52:09Z Some solutions of diophantine equation x3+y3=pk z3 2011-10 See, Kok Leong Diophantine equation is an algebraic equation in two or more variables in which solutions to it are from some predetermined classes and it is one of the oldest branches of number theory. They are studied and investigated to determine the values of the variables that satisfy the equation. This activity began since time immemorial and has developed into branches according to types of the equations. This research concentrates on investigating the solvability and the determination of representations of the integral solutions of the diophantine equation x3 + y3 = pk z3 where k is a positive integer, k º/ 0(mod3) and p = 2, 3, 5, 13. The approach used to determine the solutions of the equation is first to look for mathematical patterns of the integral solutions to the diophantine equation x3 + y3 = pk z3. Once the patterns are obtained on the forms of the solutions, general formulae are then obtained from which solutions can be acquired. Proofs are constructed to show the validity of the formulae. In our investigation, we determine the solutions to the equation for selected values of primes under certain conditions. We also determine the condition under which as equation do not have solutions. We also show that the number of solutions, if there exist, are either finite or infinite depending on the values of the associated parameter. Our work opens up other possibilities of future work that can be carried out based on the results obtained in this research. Diophantine analysis 2011-10 Thesis http://psasir.upm.edu.my/id/eprint/66457/ http://psasir.upm.edu.my/id/eprint/66457/1/IPM%202011%2022%20IR.pdf text en public masters Universiti Putra Malaysia Diophantine analysis
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Diophantine analysis
spellingShingle	Diophantine analysis See, Kok Leong Some solutions of diophantine equation x3+y3=pk z3
description	Diophantine equation is an algebraic equation in two or more variables in which solutions to it are from some predetermined classes and it is one of the oldest branches of number theory. They are studied and investigated to determine the values of the variables that satisfy the equation. This activity began since time immemorial and has developed into branches according to types of the equations. This research concentrates on investigating the solvability and the determination of representations of the integral solutions of the diophantine equation x3 + y3 = pk z3 where k is a positive integer, k º/ 0(mod3) and p = 2, 3, 5, 13. The approach used to determine the solutions of the equation is first to look for mathematical patterns of the integral solutions to the diophantine equation x3 + y3 = pk z3. Once the patterns are obtained on the forms of the solutions, general formulae are then obtained from which solutions can be acquired. Proofs are constructed to show the validity of the formulae. In our investigation, we determine the solutions to the equation for selected values of primes under certain conditions. We also determine the condition under which as equation do not have solutions. We also show that the number of solutions, if there exist, are either finite or infinite depending on the values of the associated parameter. Our work opens up other possibilities of future work that can be carried out based on the results obtained in this research.
format	Thesis
qualification_level	Master's degree
author	See, Kok Leong
author_facet	See, Kok Leong
author_sort	See, Kok Leong
title	Some solutions of diophantine equation x3+y3=pk z3
title_short	Some solutions of diophantine equation x3+y3=pk z3
title_full	Some solutions of diophantine equation x3+y3=pk z3
title_fullStr	Some solutions of diophantine equation x3+y3=pk z3
title_full_unstemmed	Some solutions of diophantine equation x3+y3=pk z3
title_sort	some solutions of diophantine equation x3+y3=pk z3
granting_institution	Universiti Putra Malaysia
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/66457/1/IPM%202011%2022%20IR.pdf
_version_	1747812385065795584

Some solutions of diophantine equation x3+y3=pk z3

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