相关论文: Some New Congruences Modulo Powers of 2 For $(j,k)…

Let $\overline{p}_{k}(n)$ denote the number of overpartition $k$-tuples of $n$. In 2023, Saikia \cite{saikia} conjectured the following congruences: \begin{align*} \overline{p}_{q}(8n+2)& \equiv 0 \pmod{4},\quad \overline{p}_{q}(8n+3)\equiv…

Let $p_{k,3}(n)$ enumerate the number of 2-color partition triples of $n$ where one of the colors appears only in parts that are multiples of $k$. In this paper, we prove several infinite families of congruences modulo powers of 3 for…

Let $p_{-k}(n)$ enumerate the number of $k$-colored partitions of $n$. In this paper, we establish some infinite families of congruences modulo 25 for $k$-colored partitions. Furthermore, we prove some infinite families of Ramanujan-type…

Let ${{\overline{p}}_{3}}(n)$ be the number of overpartition triples of $n$. By elementary series manipulations, we establish some congruences for ${\overline{p}}_{3}(n)$ modulo small powers of 2, such as…

Recently, Drema and Saikia (2023) proved several congruences modulo powers of 2 and 3 for overpartition triples with odd parts. We extend their list substantially. We prove several congruences modulo powers of 2 for overpartition k-tuples…

The starting point for this work is the family of functions $\overline{p}_{-t}(n)$ which counts the number of $t$--colored overpartitions of $n.$ In recent years, several infinite families of congruences satisfied by $\overline{p}_{-t}(n)$…

Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2023) proved several congruences modulo powers of $2$ for overpartition triples with odd parts. In this paper, we study further divisibility properties of…

For any relatively prime integers $r$ and $s$, let $a_{r,s}(n)$ denote the number of $(r,s)$-regular partitions of a positive integer of $n$ into distinct parts. Prasad and Prasad (2018) proved many infinite families of congruences modulo 2…

Let $\overline{p}(n)$ be the number of overpartitions of $n$, we establish and give a short elementary proof of the following congruence \[\overline{p}({{4}^{\alpha }}(40n+35))\equiv 0 \, (\bmod \, 40),\] where $\alpha ,n $ are nonnegative…

Inspired by the recent work by Nadji, Ahmia and Ram\'irez, we examined the arithmetic properties of $\bar{B}_{l_1,l_2} (n)$, the number of overpartitions of n whose parts are neither divisible by $l_1$ nor divisible by $l_2$. In particular,…

The enumeration $d_k(n)$ of $k$-elongated plane partition diamonds has emerged as a generalization of the classical integer partition function $p(n)$. Congruences for $d_k(n)$ modulo certain powers of primes have been proven via elementary…

Let $\overline{p}(n)$ denote the number of overpartitions of $n$. Recently, Fortin-Jacob-Mathieu and Hirschhorn-Sellers independently obtained 2-, 3- and 4-dissections of the generating function for $\overline{p}(n)$ and derived a number of…

In this paper, we establish two new Ramanujan-type congruences for the overpartition function: $\overline{p}(11\times(8n+5))\equiv 0 \pmod{11}$ and $\overline{p}(13\times 2^6(8n+7))\equiv 0 \pmod{13}$. The proofs rely on the theory of…

In this article we exhibit new explicit families of congruences for the overpartition function, making effective the existence results given previously by Treneer. We give infinite families of congruences modulo $m$ for $m = 5, 7, 11$, and…

Let $b_{\ell, k}(n), b_{\ell, k, r}(n)$ count the number of $(\ell, k)$, $(\ell, k, r)$-regular partitions respectively. In this paper we shall derive infinite families of congruences for $b_{\ell, k}(n)$ modulo $2$ when $ (\ell, k) =…

Recently, Nayaka and Naika (2022) proved several congruences modulo $16$ and $32$ for $t$-colored overpartitions with $t=5,7,11$ and $13$. We extend their list using an algorithmic technique.

Let $\overline{bt}(n)$ denote the number of overcubic partition triples of $n$. Nayaka, Dharmendra and Kumar proved some congruences modulo 8, 16 and 32 for $\overline{bt}(n)$. Recently, Saikia and Sarma established some congruences modulo…

Let $p_k(n)$ be given by the $k$-th power of the Euler Product $\prod _{n=1}^{\infty}(1-q^n)^k=\sum_{n=0}^{\infty}p_k(n)q^{n}$. By investigating the properties of the modular equations of the second and the third order under the Atkin…

In recent years, the congruence $$ \sum_{\substack{i+j+k=p\\ i,j,k>0}} \frac1{ijk} \equiv -2 B_{p-3} \pmod{p}, $$ first discovered by the last author have been generalized by either increasing the number of indices and considering the…

It is proved that the number of 9-regular partitions of n is divisible by 3 when n is congruent to 3 mod 4, and by 6 when n is congruent to 13 mod 16. An infinite family of congruences mod 3 holds in other progressions modulo powers of 4…