文摘
Let 9afb3b7a6ffbc3bbce0a" title="Click to view the MathML source">Bs,t(n) denote the number of (s,t)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for e400b32c2f" title="Click to view the MathML source">B3,11(n). She also presented several conjectures on 9afb3b7a6ffbc3bbce0a" title="Click to view the MathML source">Bs,t(n). In this paper, utilizing an theta function identity appeared in Berndt's book, we confirm three conjectures on 8ce4792d6717955ec3f7e77416fae" title="Click to view the MathML source">B3,7(n) given by Dou. Moreover, we prove several infinite families of congruences modulo 3 and 5 for B3,s(n) and b822c0e0114dd2b53313227fb" title="Click to view the MathML source">B5,s(n). In addition, we prove many infinite families of congruences modulo 7 for 8ce4792d6717955ec3f7e77416fae" title="Click to view the MathML source">B3,7(n) by employing an identity of Newman.