# On eight colour partitions

## TL;DR

This paper investigates the arithmetic properties of the 8-colour partition function, deriving new Ramanujan-type congruences modulo powers of 2 through explicit generating function formulas.

## Contribution

It introduces new Ramanujan-type congruences for the 8-colour partition function and provides explicit formulas for its generating functions.

## Key findings

- Established Ramanujan-type congruences modulo higher powers of 2.
- Derived explicit formulas for the generating functions of p_8(n).
- Enhanced understanding of the arithmetic properties of 8-colour partitions.

## Abstract

In this article, we study the arithmetic properties of the partition function $p_8(n)$, the number of 8-colour partitions of $n$. We prove several Ramanujan type congruences modulo higher powers of 2 for the function $p_8(n)$ by finding explicit formulas for the generating functions.