Balances in the Set of Arithmetic Progressions
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.
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/10/4/350 |
| _version_ | 1797506566920863744 |
|---|---|
| author | Chan-Liang Chung Chunmei Zhong Kanglun Zhou |
| author_facet | Chan-Liang Chung Chunmei Zhong Kanglun Zhou |
| author_sort | Chan-Liang Chung |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T04:34:22Z |
| format | Article |
| id | doaj.art-12d587f410ed44608c87d89d907c61a6 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T04:34:22Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-12d587f410ed44608c87d89d907c61a62023-11-23T03:50:29ZengMDPI AGAxioms2075-16802021-12-0110435010.3390/axioms10040350Balances in the Set of Arithmetic ProgressionsChan-Liang Chung0Chunmei Zhong1Kanglun Zhou2School of Mathematics and Statistics, Fuzhou University, No.2 North Road of Wulongjiang, Fuzhou 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, No.2 North Road of Wulongjiang, Fuzhou 350108, ChinaSchool of Mathematics and Statistics, Fuzhou University, No.2 North Road of Wulongjiang, Fuzhou 350108, ChinaThis 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.https://www.mdpi.com/2075-1680/10/4/350balancing numberssequence balancing numbers(<i>a</i>,<i>b</i>)-type balancing numbersPell equation |
| spellingShingle | Chan-Liang Chung Chunmei Zhong Kanglun Zhou Balances in the Set of Arithmetic Progressions Axioms balancing numbers sequence balancing numbers (<i>a</i>,<i>b</i>)-type balancing numbers Pell equation |
| title | Balances in the Set of Arithmetic Progressions |
| title_full | Balances in the Set of Arithmetic Progressions |
| title_fullStr | Balances in the Set of Arithmetic Progressions |
| title_full_unstemmed | Balances in the Set of Arithmetic Progressions |
| title_short | Balances in the Set of Arithmetic Progressions |
| title_sort | balances in the set of arithmetic progressions |
| topic | balancing numbers sequence balancing numbers (<i>a</i>,<i>b</i>)-type balancing numbers Pell equation |
| url | https://www.mdpi.com/2075-1680/10/4/350 |
| work_keys_str_mv | AT chanliangchung balancesinthesetofarithmeticprogressions AT chunmeizhong balancesinthesetofarithmeticprogressions AT kanglunzhou balancesinthesetofarithmeticprogressions |