On 2-color partitions where one of the color is multiples of 5^k

2025/03/13 by C. Shivashankar, C., Shivashankar, B. Hemanthkumar +3
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2503.10113

openalex publication_date 2025/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we investigate the arithmetic properties of p_1,5^k(n), which counts 2-color partitions of n where one of the colors appears only in parts that are multiples of 5^k. By constructing generating functions for p_1,5^k(n) across specific arithmetic progressions, we establish a set of Ramanujan-type infinite family of congruences modulo powers of 5.

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