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Regular triangular forms of rank exceeding 3.

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Title: Regular triangular forms of rank exceeding 3.
Authors: Kim, Mingyu1 (AUTHOR) mingyukim@pusan.ac.kr
Source: Journal of Number Theory. Mar2026, Vol. 280, p825-860. 36p.
Subjects: Integers, Mathematical forms, Mathematics, Quadratic equations, Polynomials, Mathematical variables
Abstract: A triangular form is an integer-valued quadratic polynomial of the form a 1 P 3 (x 1) + a 2 P 3 (x 2) + ⋯ + a k P 3 (x k) , where the coefficients a i are positive integers and P 3 (x) = x (x + 1) / 2. A triangular form is called regular if it represents all positive integers which are locally represented. In this article, we determine all regular triangular forms of more than three variables. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Number Theory is the property of Academic Press Inc. 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
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Header DbId: egs
DbLabel: Engineering Source
An: 188782719
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Regular triangular forms of rank exceeding 3.
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  Data: <searchLink fieldCode="AR" term="%22Kim%2C+Mingyu%22">Kim, Mingyu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> mingyukim@pusan.ac.kr</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Number+Theory%22">Journal of Number Theory</searchLink>. Mar2026, Vol. 280, p825-860. 36p.
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  Data: <searchLink fieldCode="DE" term="%22Integers%22">Integers</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+forms%22">Mathematical forms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+equations%22">Quadratic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+variables%22">Mathematical variables</searchLink>
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  Data: A triangular form is an integer-valued quadratic polynomial of the form a 1 P 3 (x 1) + a 2 P 3 (x 2) + ⋯ + a k P 3 (x k) , where the coefficients a i are positive integers and P 3 (x) = x (x + 1) / 2. A triangular form is called regular if it represents all positive integers which are locally represented. In this article, we determine all regular triangular forms of more than three variables. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Number Theory is the property of Academic Press Inc. 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.)
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RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1016/j.jnt.2025.09.007
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 36
        StartPage: 825
    Subjects:
      – SubjectFull: Integers
        Type: general
      – SubjectFull: Mathematical forms
        Type: general
      – SubjectFull: Mathematics
        Type: general
      – SubjectFull: Quadratic equations
        Type: general
      – SubjectFull: Polynomials
        Type: general
      – SubjectFull: Mathematical variables
        Type: general
    Titles:
      – TitleFull: Regular triangular forms of rank exceeding 3.
        Type: main
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            NameFull: Kim, Mingyu
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          Dates:
            – D: 01
              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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            – Type: issn-print
              Value: 0022314X
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              Value: 280
          Titles:
            – TitleFull: Journal of Number Theory
              Type: main
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