Regular ternary sums of generalized pentagonal numbers

The goal of this paper is to show that there are at most 42 primitive regular ternary sums of generalized pentagonal numbers and establish the regularity of all but one candidates, where the unproven candidate is [Formula: see text].

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Publication Details

Journal
International Journal of Number Theory
Published
2025-03-20
DOI
https://doi.org/10.1142/s1793042125500848
Primary Topic
Advanced Mathematical Theories and Applications
Type
article
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article

Regular ternary sums of generalized pentagonal numbers

Mingyu Kim
International Journal of Number Theory
Advanced Mathematical Theories and Applications
article

Regular ternary sums of generalized pentagonal numbers

Mingyu Kim
article en

Abstract

The goal of this paper is to show that there are at most 42 primitive regular ternary sums of generalized pentagonal numbers and establish the regularity of all but one candidates, where the unproven candidate is [Formula: see text].

International Journal of Number TheoryVol. 21(07)
Pusan National University (KR)
Reduced inequalities
Openalex Percentile: Top 95%
Advanced Mathematical Theories and Applications
DOISourceOpenAlex
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Regular ternary sums of generalized pentagonal numbers — Mingyu Kim · International Journal of Number Theory (2025) | TGRS Research Map | TGRS