Arithmetic Properties for k-Color Analogue of Simultaneously s-Regular and t-Distinct Partitions

2026/07/13 by Anjelin Mariya Johnson, S. N. Fathima
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Abstract

In this article, we discuss general generating functions for partitions of n, simultaneously s-regular and t-distinct in 3-colors. In addition, we obtain infinite families of congruences modulo powers of 3 for specific values of (ℓ,t). For instance, for positive integers n and k, we have ∑_n=o^∞RD₃^3,3(3^kn+(3^k+1)/(2))qⁿ≡0 \pmod3^k+1.

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