Quadratic Reciprocity is arguably the most important theorem taught in an elementary number theory course. Since Gauss’ original 1796 proof (by induction!) appeared, more than 100 …

We now come to the most important result in our course: the law of quadratic reciprocity, or, as Gauss called it, the aureum theorema (“golden theorem”). Many beginning students of number …

THE LAW OF QUADRATIC RECIPROCITY NIELS KETELAARS 1. Introduction The law of quadratic reciprocity is one of the most famous and important results from number theory. …

Quadratic reciprocity, Gauss. 1 This is Euler’s theorem that k is a quadratic residue (mod p)if k (p−1)/2 ≡ 1 (mod p), and k is a quadratic nonresidue (mod p)if k (p−1)/2 ≡−1 (mod p).

The law of quadratic reciprocity (the main theorem in this project) gives a precise relation- ship between the “reciprocal” Legendre symbols (p/q) and (q/p) where p,q are distinct odd primes.

Quadratic Reciprocity is arguably the most important theorem taught in an elementary number theory course. Since Gauss’ original 1796 proof (by induction!) appeared, more than 100 …

quadratic reciprocity law; Baumgart distinguished Gauss’s first proof by induction, proofs by Gauss’s Lemma, by complex analysis, by cyclotomy, and by quadratic forms.

THE LAW OF QUADRATIC RECIPROCITY BY H. D. KLOOSTERMAN (Communicated at the meeting of October 31, 1964) L. HOLZER gives in his book "Zahlentheorie" (Teil I, p. 76; …

Quadratic reciprocity 1 Introduction We now begin our next important topic, quadratic reciprocity. We have already answered the following question: Question 1: Given an odd prime p, and an …

The law of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity.

As regards the present paper, it deals with "The Law of Quadratic Reciprocity" which is considered to be the major theorem of the theory of numbers • The first section is devoted to …

We now use Gauss’s Lemma with a = q to prove the Law of Quadratic Reciprocity. Proof of Theorem 5.1. Take distinct odd primes p and q. For k = 1,2,...,p′ write (one step of the …

QUADRATIC RECIPROCITY POOJA TELAP Abstract. This paper is an self-contained exposition of the law of quadratic recipro.city eW will give wto proofs of the Chinese remainder theorem …

Given odd primes p 6= q, the Law of Quadratic Reciprocity gives an explicit relationship between the congruences x2 ≡ q (mod p) and x2 ≡ p (mod q). Euler first conjectured the Law around …

“For those who consider the theory of numbers ‘the Queen of Mathematics,’ this (Quadratic Reciprocity Law) is one of the jewels in her crown.” Gauss- first mathematician to find a …

In this thesis we will take a look at the development of the law of quadratic reciprocity. What is necessary to come up with such a theorem and what were the fundamental ideas connected …

We begin by describing what the law of quadratic reciprocity implies for quadratic number fields. K = Q[ p∗] is given by Z[ p∗]. If p∗ is a quadratic residue (mod q), say p∗ ≡ k2 (mod q), We can …

symbol long after Gauss proved the quadratic reciprocity law, similarly as Gauss invented the modulo sign long after Fermat, Euler and Lagrange proved their theorems. Exercises 1. What …