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Let Bs,t(n) denote the number of (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 B3,7(n) given by Dou. Moreover, we prove several infinite families of congruences modulo 3 and...
Let b9(n) denote the number of 9-regular partitions of n. Recently, employing the theory of modular forms, Keith established several congruences modulo 2 and 3 for b9(n). He also presented four conjectures on b9(n) and two of them have been proved by Lin, and Xia and Yao. The remaining two conjectures are b9(32n+13)≡0(mod12) and b9(64n+13)≡0(mod24) for n⩾0. In this paper, employing 2-dissection formulas...
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