文摘
Let Bs,t(n) denote the number of c20d87502155f371f6d7d199ec35" title="Click to view the MathML source">(s,t)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for B3,11(n). She also presented several conjectures on Bs,t(n). In this paper, utilizing an theta function identity appeared in Berndt's book, we confirm three conjectures on 18ce4792d6717955ec3f7e77416fae" 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 B5,s(n). In addition, we prove many infinite families of congruences modulo 7 for 18ce4792d6717955ec3f7e77416fae" title="Click to view the MathML source">B3,7(n) by employing an identity of Newman.