Arithmetic properties for cubic partition pairs modulo powers of 3

TL;DR

This paper investigates the arithmetic properties of the cubic partition pairs function, providing strategies to analyze its behavior modulo powers of 3 and confirming two of Lin's conjectures.

Contribution

It introduces a new strategy to study the arithmetic properties of cubic partition pairs and proves two conjectures posed by Lin.

Findings

Confirmed two of Lin's conjectures on cubic partition pairs.

Developed a method to analyze $b(n)$ modulo powers of 3.

Abstract

Let $b(n)$ denote the number of cubic partition pairs of $n$. In this paper, we aim to provide a strategy to obtain arithmetic properties of $b(n)$. This gives affirmative answers to two of Lin's conjectures.