Primitive Pythagorean triples and generalized Fibonacci sequences

Shannon, AG

Primitive Pythagorean triples and generalized Fibonacci sequences

Shannon, AG

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Publisher:: “Marin Drinov” Academic Publishing House of the Bulgarian Academy of Sciences
Publication Type:: Journal Article
Citation:: Notes on Number Theory and Discrete Mathematics, 2017, 23 (1), pp. 54 - 62
Issue Date:: 2017

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Field	Value	Language
dc.contributor.author	Shannon, AG https://orcid.org/0000-0003-0116-0666	en_US
dc.date.issued	2017	en_US
dc.identifier.citation	Notes on Number Theory and Discrete Mathematics, 2017, 23 (1), pp. 54 - 62	en_US
dc.identifier.issn	1310-5132	en_US
dc.identifier.uri	http://hdl.handle.net/10453/125723
dc.description.abstract	It is proved that infinite sequences of generalized Fibonacci sequences obtained from generalizations of the Golden Ratio can generate all primitive Pythagorean triples. This is a consequence of the integer structure since the major component of a primitive Pythagorean triple always has the form (4r1 + 1) where r1 belongs to the class in the modular ring Z4.	en_US
dc.publisher	“Marin Drinov” Academic Publishing House of the Bulgarian Academy of Sciences	en_US
dc.relation.ispartof	Notes on Number Theory and Discrete Mathematics	en_US
dc.title	Primitive Pythagorean triples and generalized Fibonacci sequences	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	23	en_US
utslib.for	0101 Pure 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 Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.consider-herdc	true	en_US
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	23	en_US

Abstract:

It is proved that infinite sequences of generalized Fibonacci sequences obtained from generalizations of the Golden Ratio can generate all primitive Pythagorean triples. This is a consequence of the integer structure since the major component of a primitive Pythagorean triple always has the form (4r1 + 1) where r1 belongs to the class in the modular ring Z4.

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http://hdl.handle.net/10453/125723