Arithmetic properties for two restricted partitions modulo powers of 5. Issue 2 (1st February 2020)

• Record Type: Journal Article
• Authors: Tang, Dazhao
• Is Part Of: Quaestiones mathematicae. Volume 43:Issue 2(2020)
• Page Start: 169
• Page End: 183
• Publication Date: 2020-02-01
• Subjects: 05A17 -- 11P83; Partition -- congruences -- 2-color partition triples -- (k, ℓ)-regular bipartitions; Mathematics -- Periodicals; 510.5
• DOI: 10.2989/16073606.2018.1544945
• Languages: English
• ISSNs: 1607-3606

Abstract

Abstract: Let pk, 3 ( n ) count the number of 2-color partition triples of n where one of the colors appears only in parts that are multiples of k and Bk, ℓ ( n ) denote the number of ( k, ℓ )-regular bipartitions of n . In this paper, we prove two infinite families of congruences modulo 5 for p 5, 3 ( n ), three infinite families of congruences modulo powers of 5 for p 25, 3 ( n ), and six infinite families of congruences modulo powers of 5 for B 5, 25 ( n ). For instance, for any integers n ≥ 0 and α ≥ 1, we have and