Abstract
We define (Formula presented) 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 (Formula presented). In the concluding remarks of their paper, they conjectured that (Formula presented) 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 (Formula presented) previously proven via the machinery of modular forms by Alanazi, Munagi, and Saikia [arXiv:2412.18938 [math.NT], (2024)].
| Original language | English (US) |
|---|---|
| Pages (from-to) | 80-87 |
| Number of pages | 8 |
| Journal | Discrete Mathematics Letters |
| Volume | 16 |
| DOIs | |
| State | Published - 2025 |
Bibliographical note
Publisher Copyright:© 2025, Shahin Digital Publisher. All rights reserved.
Keywords
- congruence
- generating function
- overpartition
- partition
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