English

Some congruences for $(s,t)$-regular bipartitions modulo $t$

Number Theory 2019-10-16 v2

Abstract

In this work, we study the function Bs,t(n)B_{s,t}(n), which counts the number of (s,t)(s,t)-regular bipartitions of nn. Recently, many authors proved infinite families of congruences modulo 1111 for B3,11(n)B_{3,11}(n), modulo 33 for B3,s(n)B_{3,s}(n) and modulo 55 for B5,s(n)B_{5,s}(n). Very recently, Kathiravan proved several infinite families of congruences modulo 1111, 1313 and 1717 for B5,11(n)B_{5,11}(n), B5,13(n)B_{5,13}(n) and B81,17(n)B_{81,17}(n). In this paper, we will prove infinite families of congruences modulo 55 for B2,15(n)B_{2,15}(n), modulo 1111 for B7,11(n)B_{7,11}(n), modulo 1111 for B27,11(n)B_{27,11}(n) and modulo 1717 for B243,17(n)B_{243,17}(n).

Keywords

Cite

@article{arxiv.1908.06642,
  title  = {Some congruences for $(s,t)$-regular bipartitions modulo $t$},
  author = {T. Kathiravan and K. Srilakshmi},
  journal= {arXiv preprint arXiv:1908.06642},
  year   = {2019}
}

Comments

arXiv admin note: text overlap with arXiv:1907.13450

R2 v1 2026-06-23T10:50:36.646Z