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arXiv · 2504.06941

Proofs of two conjectures on congruences of overcubic partition triples

Jiayu Chen·Jing Jin·Olivia X. M. Yao
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Abstract

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 64 for $\overline{bt}(n)$ by using both elementary techniques and the theory of modular forms. In their paper, they also posed two conjectures on infinite families of congruences modulo 64 and 128 for $\overline{bt}(n)$. In this paper, we confirm the two conjectures.

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Jiayu Chen, Jing Jin, Olivia X. M. Yao. 2025-04-09. Proofs of two conjectures on congruences of overcubic partition triples. https://arxiv.org/abs/2504.06941

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