Congruences modulo powers of 5 for k-colored partitions

2017/11/07 by Dazhao Tang, Tang, Dazhao
Mathematics · #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1711.02325

openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 α≥1, we prove that p_-2(5^2α-1n+\dfrac7×5^2α-1+112) amp;≡0\pmod5^α and p_-2(5^2αn+\dfrac11×5^2α+112) amp;≡0\pmod5^α+1.

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