Elementary Proofs of Recent Congruences for Overpartitions Wherein Non-Overlined Parts are Not Divisible by 6
Abstract
Elementary methods are used to confirm conjectured congruences for overpartitions with non-overlined parts not divisible by 6 and to reprove previously established congruences.
We define R_l^*(n) as the number of overpartitions of n in which non-overlined parts are not divisible by l. In a recent work, Nath, Saikia, and the second author established several families of congruences for R_l^*(n), with particular focus on the cases l=6 and l=8. In the concluding remarks of their paper, they conjectured that R_6^*(n) satisfies an infinite family of congruences modulo 128. In this paper, we confirm their conjectures using elementary methods. Additionally, we provide elementary proofs of two congruences for R_6^*(n) previously proven via the machinery of modular forms by Alanazi, Munagi, and Saikia.
Models citing this paper 0
No model linking this paper
Datasets citing this paper 1
Spaces citing this paper 0
No Space linking this paper
Collections including this paper 0
No Collection including this paper