Congruences modulo powers of 5 for k-colored partitions

JOURNAL OF NUMBER THEORY

卷:187

Article

Tang, Dazhao¹ 

[1] Chongqing Univ, Coll Math & Stat, Huxi Campus LD206, Chongqing 401331, Peoples R China

关键词: Partition;    Congruences;    k-Colored partitions;   

DOI  :  10.1016/j.jnt.2017.10.027

来源: Elsevier

【 摘 要 】

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 congruences modulo powers of 5 for (p-k)(n) with k = 2, 6, and 7. For example, for all integers n >= 0 and alpha >= 1, we prove that p-2 (5(2 alpha-1)n + 7 x 5(2 alpha-1) + 1/12) equivalent to 0 (mod 5(alpha)) and p-2 (5(2 alpha)n + 11 x 5(2 alpha) + 1/12) equivalent to 0 (mod 5(alpha+1)). (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free