On rational numbers with nonterminating p-adic continued fraction expansion.
Saved in:
| Title: | On rational numbers with nonterminating p-adic continued fraction expansion. |
|---|---|
| Authors: | PEJKOVIĆ, Tomislav1 |
| Source: | Proceedings of the Japan Academy, Series A: Mathematical Sciences. Apr2026, Vol. 102 Issue 4, p17-23. 7p. |
| Subjects: | Continued fractions, Rational numbers, Number theory, Prime numbers, Number systems |
| Abstract: | We determine all pairs (p, n), where p is a prime and n a positive integer, such that there exists a reduced fraction u/v > 1 with u + v = n and u/v has a nonterminating Schneider's p-adic continued fraction expansion. We also prove a bound on the length of the preperiod in the p-adic continued fraction of u/v when max{|u|, |v|} < p. [ABSTRACT FROM AUTHOR] |
| Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Links: – Type: pdflink Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 192912132 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: On rational numbers with nonterminating p-adic continued fraction expansion. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22PEJKOVIĆ%2C+Tomislav%22">PEJKOVIĆ, Tomislav</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Japan+Academy%2C+Series+A%3A+Mathematical+Sciences%22">Proceedings of the Japan Academy, Series A: Mathematical Sciences</searchLink>. Apr2026, Vol. 102 Issue 4, p17-23. 7p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Continued+fractions%22">Continued fractions</searchLink><br /><searchLink fieldCode="DE" term="%22Rational+numbers%22">Rational numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Number+theory%22">Number theory</searchLink><br /><searchLink fieldCode="DE" term="%22Prime+numbers%22">Prime numbers</searchLink><br /><searchLink fieldCode="DE" term="%22Number+systems%22">Number systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We determine all pairs (p, n), where p is a prime and n a positive integer, such that there exists a reduced fraction u/v > 1 with u + v = n and u/v has a nonterminating Schneider's p-adic continued fraction expansion. We also prove a bound on the length of the preperiod in the p-adic continued fraction of u/v when max{|u|, |v|} < p. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Proceedings of the Japan Academy, Series A: Mathematical Sciences is the property of Japan Academy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=192912132 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3792/pjaa.102.004 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 7 StartPage: 17 Subjects: – SubjectFull: Continued fractions Type: general – SubjectFull: Rational numbers Type: general – SubjectFull: Number theory Type: general – SubjectFull: Prime numbers Type: general – SubjectFull: Number systems Type: general Titles: – TitleFull: On rational numbers with nonterminating p-adic continued fraction expansion. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: PEJKOVIĆ, Tomislav IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 04 Text: Apr2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03862194 Numbering: – Type: volume Value: 102 – Type: issue Value: 4 Titles: – TitleFull: Proceedings of the Japan Academy, Series A: Mathematical Sciences Type: main |
| ResultId | 1 |
