The Fermat's and Euler's congruence theorems

TL;DR

This paper presents explicit formulas for translation symmetries in Cartesian products and derives fundamental results in elementary number theory, contributing to the understanding of symmetry and number theoretic properties.

Contribution

It introduces explicit formulas for translation symmetries in Cartesian products and provides new elementary number theory results.

Findings

Explicit formulas for translation symmetries in Cartesian products

Fundamental results in elementary number theory derived

Enhanced understanding of symmetry in finite sets

Abstract

We give an explicit formulae for obtaining the translation symmetries in the cartesian product $X^N$, where $N$ is some positive integer and $X$ is some finite set. Moreover, we obtain some fundamental results from elementary number theory.