# Eulerian Composition of Certain Franklin Squares

## TL;DR

This paper investigates Franklin squares by decomposing them into quotient and remainder components, providing evidence that Eulerian composition was used in their construction and demonstrating how to create new Franklin squares using this method.

## Contribution

It offers a decomposition approach supporting the Eulerian composition method as a construction technique for Franklin squares and introduces a way to generate new squares.

## Key findings

- Decomposition of Franklin squares into quotient and remainder squares.
- Support for Eulerian composition as a construction method.
- Method to construct new Franklin squares.

## Abstract

Several specific Franklin squares and magic squares are decomposed into their quotient and remainder squares. The results support the conjecture that Franklin used the Eulerian composition method to construct many of his squares. This method also can be used to construct new Franklin squares as illustrated herein.