Hermite's identity and the quadratic reciprocity law

TL;DR

This paper presents a concise proof of the quadratic reciprocity law by leveraging Gauss's Lemma and Hermite's identity, simplifying the understanding of this fundamental number theory result.

Contribution

It introduces a novel, streamlined proof of quadratic reciprocity utilizing classical identities, enhancing pedagogical clarity and mathematical elegance.

Findings

Simplified proof of quadratic reciprocity law

Application of Hermite's identity in number theory

Clarification of classical number theory concepts

Abstract

We give a short proof of the quadratic reciprocity law using Gauss's Lemma and Hermite's identity.