Universal sums of generalized heptagonal numbers

被引：0

作者：

Kamaraj, Ramanujam ^{[1
]}

Kane, Ben ^{[1
]}

Oishi-Tomiyasu, Ryoko ^{[2
]}

机构：

[1] Univ Hong Kong, Dept Math, Pokfulam, Hong Kong, Peoples R China

[2] Kyushu Univ, Inst Math Ind, Kyushu, Japan

来源：

JOURNAL OF NUMBER THEORY | 2023年 / 249卷

关键词：

Diophantine equations; Sums of polygonal numbers; Theta functions; Quadratic forms; QUADRATIC-FORMS;

D O I：

10.1016/j.jnt.2023.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider representations of integers as sums of heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such sums which are universal, i.e., those that represent every positive integer. We prove an explicit finite bound such that a given sum is universal if and only if it represents positive integer up to the given bound. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：500 / 536

页数：37

共 50 条

[21] Powers of Two as Sums of Three Pell Numbers
Bravo, Jhon J.
Faye, Bernadette
Luca, Florian
TAIWANESE JOURNAL OF MATHEMATICS, 2017, 21 (04): : 739 - 751
[22] Generalized Knopp identities for homogeneous Hardy sums and Cochrane-Hardy sums
Liu, Huaning
Gao, Jing
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2012, 62 (04) : 1147 - 1159
[23] An identity of Ramanujan and the representation of integers as sums of triangular numbers
Liu, ZG
RAMANUJAN JOURNAL, 2003, 7 (04): : 407 - 434
[24] ON FACTORIALS EXPRESSIBLE AS SUMS OF AT MOST THREE FIBONACCI NUMBERS
Luca, Florian
Siksek, Samir
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2010, 53 : 747 - 763
[25] ON THE STRONG LAW OF LARGE NUMBERS FOR WEIGHTED SUMS OF NEGATIVELY SUPERADDITIVE DEPENDENT RANDOM VARIABLES
Shen, Aiting
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 53 (01) : 45 - 55
[26] PERFECT POWERS THAT ARE SUMS OF TWO POWERS OF FIBONACCI NUMBERS
Zhang, Zhongfeng
Togbe, Alain
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2019, 99 (01) : 34 - 41
[27] REPDIGITS IN THE BASE b AS SUMS OF FOUR BALANCING NUMBERS
Keskin, Refik
Erduvan, Fatih
MATHEMATICA BOHEMICA, 2021, 146 (01): : 55 - 68
[28] An Identity of Ramanujan and the Representation of Integers as Sums of Triangular Numbers
Zhi-Guo Liu
The Ramanujan Journal, 2003, 7 : 407 - 434
[29] Cullen numbers and Woodall numbers in generalized Fibonacci sequences
Berczes, Attila
Pink, Istvan
Young, Paul Thomas
JOURNAL OF NUMBER THEORY, 2024, 262 : 86 - 102
[30] Curious properties of generalized Lucas numbers
Hashim, Hayder R.
BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2021, 27 (03):

← 1 2 3 4 5 →