# A Platonic basis of Integers

## TL;DR

This paper demonstrates that all integers can be expressed as a combination of four tetrahedral numbers and explores the modular periodicity of platonic numbers.

## Contribution

It establishes a new representation theorem for integers using tetrahedral numbers and analyzes the modular properties of platonic numbers.

## Key findings

- Every integer can be written as an integer combination of four tetrahedral numbers.
- Computed the modular periodicity of platonic numbers.
- Provided theoretical insights into the structure of platonic numbers.

## Abstract

In this article, we prove that every integer can be written as an integer combination of exactly 4 tetrahedral numbers. Moreover, we compute the modular periodicity of platonic numbers.