On continued fraction partial quotients of square roots of primes

2023
journal article
article
dc.abstract.enWe show that for each positive integer a there exist only finitely many prime numbers p such that a appears an odd number of times in the period of continued fraction of or . We also prove that if p is a prime number and or 2p is such that the length of the period of continued fraction expansion of is divisible by 4, then 1 appears as a partial quotient in the continued fraction of . Furthermore, we give an upper bound for the period length of continued fraction expansion of , where D is a positive non-square, and factorize some family of polynomials with integral coefficients connected with continued fractions of square roots of positive integers. These results answer several questions recently posed by Miska and Ulas [MU].pl
dc.affiliationWydział Matematyki i Informatyki : Instytut Matematykipl
dc.contributor.authorKala, Vítězslavpl
dc.contributor.authorMiska, Piotr - 191205 pl
dc.date.accessioned2023-08-21T11:15:55Z
dc.date.available2023-08-21T11:15:55Z
dc.date.issued2023pl
dc.date.openaccess0
dc.description.accesstimew momencie opublikowania
dc.description.physical215-234pl
dc.description.versionostateczna wersja wydawcy
dc.description.volume253pl
dc.identifier.doi10.1016/j.jnt.2023.06.013pl
dc.identifier.eissn1096-1658pl
dc.identifier.issn0022-314Xpl
dc.identifier.urihttps://ruj.uj.edu.pl/xmlui/handle/item/317828
dc.languageengpl
dc.language.containerengpl
dc.rightsUdzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa*
dc.rights.licenceCC-BY
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/legalcode.pl*
dc.share.typeinne
dc.subject.encontinued fractionpl
dc.subject.enprime numberpl
dc.subject.ensquare root of a positive integerpl
dc.subtypeArticlepl
dc.titleOn continued fraction partial quotients of square roots of primespl
dc.title.journalJournal of Number Theorypl
dc.typeJournalArticlepl
dspace.entity.typePublication
dc.abstract.enpl
We show that for each positive integer a there exist only finitely many prime numbers p such that a appears an odd number of times in the period of continued fraction of or . We also prove that if p is a prime number and or 2p is such that the length of the period of continued fraction expansion of is divisible by 4, then 1 appears as a partial quotient in the continued fraction of . Furthermore, we give an upper bound for the period length of continued fraction expansion of , where D is a positive non-square, and factorize some family of polynomials with integral coefficients connected with continued fractions of square roots of positive integers. These results answer several questions recently posed by Miska and Ulas [MU].
dc.affiliationpl
Wydział Matematyki i Informatyki : Instytut Matematyki
dc.contributor.authorpl
Kala, Vítězslav
dc.contributor.authorpl
Miska, Piotr - 191205
dc.date.accessioned
2023-08-21T11:15:55Z
dc.date.available
2023-08-21T11:15:55Z
dc.date.issuedpl
2023
dc.date.openaccess
0
dc.description.accesstime
w momencie opublikowania
dc.description.physicalpl
215-234
dc.description.version
ostateczna wersja wydawcy
dc.description.volumepl
253
dc.identifier.doipl
10.1016/j.jnt.2023.06.013
dc.identifier.eissnpl
1096-1658
dc.identifier.issnpl
0022-314X
dc.identifier.uri
https://ruj.uj.edu.pl/xmlui/handle/item/317828
dc.languagepl
eng
dc.language.containerpl
eng
dc.rights*
Udzielam licencji. Uznanie autorstwa 4.0 Międzynarodowa
dc.rights.licence
CC-BY
dc.rights.uri*
http://creativecommons.org/licenses/by/4.0/legalcode.pl
dc.share.type
inne
dc.subject.enpl
continued fraction
dc.subject.enpl
prime number
dc.subject.enpl
square root of a positive integer
dc.subtypepl
Article
dc.titlepl
On continued fraction partial quotients of square roots of primes
dc.title.journalpl
Journal of Number Theory
dc.typepl
JournalArticle
dspace.entity.type
Publication
Affiliations

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