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

  • Thread starter Thread starter mitchell2007
  • Start date Start date
Click For Summary
N-reciprocity extends classical results in number theory, particularly those of Gauss, by exploring the relationships between distinct primes p and q through modular equations. The discussion centers on the implications of the equations x^n ≡ p (mod q) and x^n ≡ q (mod p) for all positive integers n. This concept aims to generalize reciprocity theorems, potentially revealing deeper connections in number theory. The significance lies in its ability to unify various results and provide new insights into prime relationships. Overall, N-reciprocity represents a promising area of exploration in advancing mathematical understanding.
mitchell2007
Messages
6
Reaction score
0
generalizing Gauss and others results could we speak of a nreciprocity involving the 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

Thread 'Confusion about the Moyal-Weyl twist'

I am studying the mathematical formalism behind non-commutative geometry approach to quantum gravity. I was reading about Hopf algebras and their Drinfeld twist with a specific example of the Moyal-Weyl twist defined as F=exp(-iλ/2θ^(μν)∂_μ⊗∂_ν) where λ is a constant parametar and θ antisymmetric constant tensor. {∂_μ} is the basis of the tangent vector space over the underlying spacetime Now, from my understanding the enveloping algebra which appears in the definition of the Hopf algebra...
View full post »

Similar threads

Undergrad How to show ##p(x)=g(x)x\pm 1\in\Bbb{Q}[x]## is irreducible in ##\Bbb{Q}_{\Bbb{Z}}[x]##?
  • · Replies 48 ·
2
Replies
48
Views
4K
Undergrad Understanding the Results of gcd(x,n)
  • · Replies 8 ·
Replies
8
Views
2K
For n>3, show that the integers n, n+2, n+4 cannot all be prime
  • · Replies 27 ·
Replies
27
Views
3K
Number of quadratic residues mod N>1
  • · Replies 3 ·
Replies
3
Views
4K
Undergrad Questions about non existence of GCDs vs (coimages, cokernels)
  • · Replies 12 ·
Replies
12
Views
636
Algorithm to find square root of a quadratic residue mod p
  • · Replies 2 ·
Replies
2
Views
2K
Problem about Fermat numbers and order of an element
  • · Replies 4 ·
Replies
4
Views
3K
A question about quadratic residues
  • · Replies 1 ·
Replies
1
Views
3K
Proof of A^(de) = a mod n for All Integers a
  • · Replies 1 ·
Replies
1
Views
2K
High School Probability that 2 distinct integers are divisible by the same number
  • · Replies 9 ·
Replies
9
Views
2K