Elementary proofs of recent congruences for overpartitions wherein non-overlined parts are not divisible by 6
Year: 2025
Type: article
Abstract: 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 [arXiv:2503.12145v2[math.NT], (2025)] established several families of congruences for R * l (n).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 [arXiv:2412.18938[math.
Source: Discrete Mathematics Letters
Authors: Bishnu Paudel, James A. Sellers, Haiyang Wang
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4417147120
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