What is N-Reciprocity and its significance in number theory?

Thread starter mitchell2007
Start date Feb 23, 2007

Feb 23, 2007

mitchell2007

generalizing Gauss and others results could we speak of a nreciprocity involving teh solution (p and q are distinct primes) of x^{n} \equiv p mod (q) and x^{n} \equiv q mod (p ) where n is every positive integer.

Physics news on Phys.org

Feb 23, 2007

DeadWolfe

http://mathworld.wolfram.com/ReciprocityTheorem.html

Thread 'The colorful world of ##2\times 2## complex matrices'

The world of 2\times 2 complex matrices is very colorful. They form a Banach-algebra, they act on spinors, they contain the quaternions, SU(2), su(2), SL(2,\mathbb C), sl(2,\mathbb C). Furthermore, with the determinant as Euclidean or pseudo-Euclidean norm, isu(2) is a 3-dimensional Euclidean space, \mathbb RI\oplus isu(2) is a Minkowski space with signature (1,3), i\mathbb RI\oplus su(2) is a Minkowski space with signature (3,1), SU(2) is the double cover of SO(3), sl(2,\mathbb C) is the...

View full post »

Thread 'About the existence of Hamel basis for vector spaces'

It is well known that a vector space always admits an algebraic (Hamel) basis. This is a theorem that follows from Zorn's lemma based on the Axiom of Choice (AC). Now consider any specific instance of vector space. Since the AC axiom may or may not be included in the underlying set theory, might there be examples of vector spaces in which an Hamel basis actually doesn't exist ?

View full post »

Thread 'When are Markov Matrices also Martingales?'

Are there known conditions under which a Markov Chain is also a Martingale? I know only that the only Random Walk that is a Martingale is the symmetric one, i.e., p= 1-p =1/2.

View full post »

Similar threads

I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

Jul 23, 2025

Replies: 48

Views: 4K

I Understanding the Results of gcd(x,n)

Oct 19, 2021

Replies: 8

Views: 2K

For n>3, show that the integers n, n+2, n+4 cannot all be prime

Apr 27, 2022

Replies: 27

Views: 3K

Number of quadratic residues mod N>1

Sep 13, 2014

Replies: 3

Views: 4K

I Questions about non existence of GCDs vs (coimages, cokernels)

Sep 3, 2025

Replies: 12

Views: 271

Algorithm to find square root of a quadratic residue mod p

Feb 19, 2015

Replies: 2

Views: 2K

Problem about Fermat numbers and order of an element

Nov 14, 2011

Replies: 4

Views: 3K

A question about quadratic residues

Mar 17, 2012

Replies: 1

Views: 3K

Proof of A^(de) = a mod n for All Integers a

Jul 24, 2009

Replies: 1

Views: 2K

B Probability that 2 distinct integers are divisible by the same number

Oct 29, 2024

Replies: 9

Views: 2K

Bluesky LinkedIn

What is N-Reciprocity and its significance in number theory?

Thread 'The colorful world of ##2\times 2## complex matrices'

Thread 'About the existence of Hamel basis for vector spaces'

Thread 'When are Markov Matrices also Martingales?'

Similar threads

Hot Threads

I How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?

I Showing ##k[x_1,\ldots,x_n]/\mathfrak{a}## is finite dimensional

I How do we distinguish two different notations for cokernel and coimage?

I Localising a non integral domain at a prime

I ##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?

Recent Insights

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Insights What Exactly is Dirac’s Delta Function? - Insight

Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

Insights Fixing Things Which Can Go Wrong With Complex Numbers