A Proof of Euler's Theorem via Quandles

TL;DR

This paper presents a novel proof of Euler's theorem in number theory using quandles, an algebraic structure inspired by knot theory, bridging concepts from algebra and topology.

Contribution

Introduces a new proof of Euler's theorem leveraging quandles, connecting number theory with knot theory structures.

Findings

Euler's theorem proved using quandles

Establishes a link between algebraic topology and number theory

Demonstrates the applicability of quandles beyond knot theory

Abstract

We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.