A Minimalist Proof of the Law of Quadratic Reciprocity

TL;DR

This paper presents the shortest known proof of the law of quadratic reciprocity, a fundamental result in number theory, without using supplements, simplifying previous proofs.

Contribution

It provides a minimalist proof of quadratic reciprocity, removing the need for supplementary lemmas or complex arguments.

Findings

Shortest known proof of quadratic reciprocity

Simplifies understanding of the law

Eliminates reliance on supplements

Abstract

The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.