Congruences for (2, 5)-regular Bipartitions into Distinct Parts

M. Prasad1, S. R. Nayaka1 and K. V. Prasad2

1Department of Mathematics, PES College of Engineering, Mandya, Karnataka, India.
2Department of Mathematics, VSK University, Ballary, Karnataka, India.

Abstract: Let $B_{2, 5}(n)$ denote the number of $(2, 5)$-regular bipartitions of a positive integer $n$ into distinct parts . In this paper, we establish several infinite families of congruences modulo powers of $2$ for $B_{2, 5}(n)$. For example, \begin{equation*} \sum_{n=0}^{\infty}B_{2, 5}\left(2^{2\alpha+1}\cdot5^{2\beta}n+\frac{2^{2\alpha+2}\cdot5^{2\beta}-1}{3}\right)q^n \equiv 2f_1f_{5}^3 \pmod{2^2}, \end{equation*} for $\alpha, \beta \geq 0$.
Keywords: Partition identities, Theta--functions, Partition congruences, Regular partition.

Cite this article as: M. Prasad, S. R. Nayaka and K. V. Prasad, Congruences for (2, 5)-regular Bipartitions into Distinct Parts, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 17-25.

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