Pellian sequences and squares

Leyendekkers, J; Shannon, AG

Pellian sequences and squares

Leyendekkers, J Shannon, AG

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Publisher:: NNTM
Publication Type:: Journal Article
Citation:: Notes on Intuitionistic Fuzzy Sets, 2012, 18 (4), pp. 7 - 10
Issue Date:: 2012-01

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Field	Value	Language
dc.contributor.author	Leyendekkers, J	en_US
dc.contributor.author	Shannon, AG	en_US
dc.date.issued	2012-01	en_US
dc.identifier.citation	Notes on Intuitionistic Fuzzy Sets, 2012, 18 (4), pp. 7 - 10	en_US
dc.identifier.issn	1310-5132	en_US
dc.identifier.uri	http://hdl.handle.net/10453/22773
dc.description.abstract	Elements of the Pell sequence satisfy a class of second order linear recurrence relations which interrelate a number of integer properties, such as elements of the rows of even and odd squares in the modular ring Z4. Integer Structure Analysis of this yields multiple-square equations exemplified by primitive Pythagorean triples, the Hoppenot equation and the equation for a sphere centred at the origin. The structure breaks down for higher powered triples so that solutions are blocked. However, Eulers extension of Fermats Last Theorem does not work as the structure does permit multiple power equations such as a 5 + b 5 + c 5 + d 5 = e 5	en_US
dc.publisher	NNTM	en_US
dc.relation.ispartof	Notes on Intuitionistic Fuzzy Sets	en_US
dc.relation.isbasedon	10.1016/j.endm.2013.07.006	en_US
dc.subject.classification	Computation Theory & Mathematics	en_US
dc.title	Pellian sequences and squares	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	18	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0802 Computation Theory and Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
utslib.copyright.status	closed_access
pubs.consider-herdc	true	en_US
pubs.issue	4	en_US
pubs.volume	18	en_US

Abstract:

Elements of the Pell sequence satisfy a class of second order linear recurrence relations which interrelate a number of integer properties, such as elements of the rows of even and odd squares in the modular ring Z4. Integer Structure Analysis of this yields multiple-square equations exemplified by primitive Pythagorean triples, the Hoppenot equation and the equation for a sphere centred at the origin. The structure breaks down for higher powered triples so that solutions are blocked. However, Eulers extension of Fermats Last Theorem does not work as the structure does permit multiple power equations such as a 5 + b 5 + c 5 + d 5 = e 5

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http://hdl.handle.net/10453/22773