A proof of the Quadratic Reciprocity Law

TL;DR

This paper provides a proof of the Quadratic Reciprocity Law utilizing Gauss's lemma, finite field theory, and the Frobenius automorphism, offering a modern algebraic perspective.

Contribution

It introduces a novel proof of the Quadratic Reciprocity Law based on finite field theory and Frobenius automorphism, expanding the algebraic methods used in number theory.

Findings

Proof leverages finite fields and Frobenius automorphism

Connects classical Gauss lemma with modern algebraic concepts

Provides a new algebraic perspective on quadratic reciprocity

Abstract

A proof of the Quadratic Reciprocity Law is presented using a Lemma of Gauss, the theory of finite fields and the Frobenius automorfism.