Balances in the Set of Arithmetic Progressions

被引：0

作者：

Chung, Chan-Liang ^{[1
]}

Zhong, Chunmei ^{[1
]}

Zhou, Kanglun ^{[1
]}

机构：

[1] Fuzhou Univ, Sch Math & Stat, 2 North Rd Wulongjiang, Fuzhou 350108, Peoples R China

来源：

AXIOMS | 2021年 / 10卷 / 04期

关键词：

balancing numbers; sequence balancing numbers; (a; b)-type balancing numbers; Pell equation;

D O I：

10.3390/axioms10040350

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article focuses on searching and classifying balancing numbers in a set of arithmetic progressions. The sufficient and necessary conditions for the existence of balancing numbers are presented. Moreover, explicit formulae of balancing numbers and various relations are included.

引用

页数：9

共 50 条

[31] DISJOINT ARITHMETIC PROGRESSIONS
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[J]. AMERICAN MATHEMATICAL MONTHLY, 1990, 97 (03): : 247 - 248
[32] ON WEAKLY ARITHMETIC PROGRESSIONS
HARZHEIM, E
[J]. DISCRETE MATHEMATICS, 1995, 138 (1-3) : 255 - 260
[33] Partitioning by arithmetic progressions
Dutch, K
[J]. AMERICAN MATHEMATICAL MONTHLY, 2005, 112 (01): : 89 - 90
[34] PRIMES IN ARITHMETIC PROGRESSIONS
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[J]. MICHIGAN MATHEMATICAL JOURNAL, 1966, 13 (04) : 485 - +
[35] Powers in arithmetic progressions
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[36] AVOIDANCE OF ARITHMETIC PROGRESSIONS
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[J]. AMERICAN MATHEMATICAL MONTHLY, 1989, 96 (01): : 63 - 64
[37] Arithmetic progressions in sumsets
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[38] DENSITIES IN ARITHMETIC PROGRESSIONS
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[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1968, 19 (06) : 1389 - +
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[40] PRIMES IN ARITHMETIC PROGRESSIONS
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IWANIEC, H
[J]. ACTA ARITHMETICA, 1983, 42 (02) : 197 - 218

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