Extending theorems of Serret and Pavone

dc.contributor.author	Matthews, Keith R.	es-ES
dc.contributor.author	Robertson, John P.	es-ES
dc.contributor.author	Srinivasan, Anitha	es-ES
dc.date.accessioned	2024-08-29T11:53:54Z
dc.date.available	2024-08-29T11:53:54Z
dc.date.issued	2017-01-01	es_ES
dc.identifier.issn	1530-7638	es_ES
dc.identifier.uri	http://hdl.handle.net/11531/92502
dc.description	Artículos en revistas	es_ES
dc.description.abstract	.	es-ES
dc.description.abstract	We extend theorems of Serret and Pavone for solving f(x, y) = ax2+bxy+cy2 = µ, where a > 0, gcd(x, y) = 1, y > 0. Here d = b2 - 4ac > 0 is not a perfect square and 0 < \|µ\| < √d/2. If µ > 0, Serret proved that x/y is a convergent to ρ = (-b+√d)/2a or σ = (-b - √d)/2a. If µ < 0, we are able to modify Pavone’s approach and show that with at most one exception, the solutions are convergents to ρ or σ.	en-GB
dc.format.mimetype	application/pdf	es_ES
dc.language.iso	en-GB	es_ES
dc.rights		es_ES
dc.rights.uri		es_ES
dc.source	Revista: Journal of integer sequences, Periodo: 1, Volumen: 20, Número: 101, Página inicial: 17.10.5, Página final: .	es_ES
dc.title	Extending theorems of Serret and Pavone	es_ES
dc.type	info:eu-repo/semantics/article	es_ES
dc.description.version	info:eu-repo/semantics/publishedVersion	es_ES
dc.rights.holder	preguntar autora	es_ES
dc.rights.accessRights	info:eu-repo/semantics/restrictedAccess	es_ES
dc.keywords	.	es-ES
dc.keywords	Continued fraction; Convergent; Fundamental solution; Indefinite binary quadratic form; Quadratic diophantine equation	en-GB

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