Introduction: Solving the General Quadratic Congruence Modulo a Prime

2016 ◽  
pp. 1-8
Author(s):  
Steve Wright
Keyword(s):  
Congruence Modulo ◽  
Quadratic Congruence

scholarly journals RP-179: Formulation of Solutions of Standard Bi-Quadratic Congruence Modulo a POSITIVE INTEGER MULTIPLE to nth Power of Four

2021 ◽  
Vol 9 (VII) ◽  
pp. 2598-2601
Author(s):  
Prof. B. M. Roy
Keyword(s):  
Positive Integer ◽  
Integer Multiple ◽  
Composite Modulus ◽  
First Case ◽  
Congruence Modulo ◽  
Quadratic Congruence ◽  
First Time

In this paper, the author has formulated the solutions of the standard bi-quadratic congruence of an even composite modulus modulo a positive integer multiple to nth power of four. First time a formula is established for the solutions. No literature is available for the current congruence. The author analysed the formulation of solutions in two different cases. In the first case of analysis, the congruence has the formulation which gives exactly eight incongruence solutions while in the second case of the analysis, the congruence has a different formulation of solutions and gives thirty-two incongruent solutions. A very simple and easy formulation to find all the solutions is presented here. Formulation is the merit of the paper.

Algorithms for the Solution of the Quadratic Congruence

1929 ◽  
Vol 36 (2) ◽  
pp. 83
Author(s):  
H. S. Vandiver
Keyword(s):  
Quadratic Congruence

An Improved Outsourcing Algorithm to Solve Quadratic Congruence Equations in Internet of Things

2021 ◽  
pp. 1-1
Author(s):  
Xiulan Li ◽  
Jingguo Bi ◽  
Chengliang Tian ◽  
Hanlin Zhang ◽  
Jia Yu ◽  
...  
Keyword(s):  
Internet Of Things ◽  
Quadratic Congruence ◽  
Outsourcing Algorithm

On the number of incongruent solutions to a quadratic congruence over algebraic integers

2019 ◽  
Vol 15 (01) ◽  
pp. 105-130
Author(s):  
Ramy F. Taki Eldin
Keyword(s):  
Prime Ideal ◽  
Number Field ◽  
Exponential Sums ◽  
Nonzero Ideal ◽  
Explicit Formulas ◽  
Algebraic Integers ◽  
Ideal Formula ◽  
Quadratic Congruence ◽  
Ring Of Algebraic Integers

Over the ring of algebraic integers [Formula: see text] of a number field [Formula: see text], the quadratic congruence [Formula: see text] modulo a nonzero ideal [Formula: see text] is considered. We prove explicit formulas for [Formula: see text] and [Formula: see text], the number of incongruent solutions [Formula: see text] and the number of incongruent solutions [Formula: see text] with [Formula: see text] coprime to [Formula: see text], respectively. If [Formula: see text] is contained in a prime ideal [Formula: see text] containing the rational prime [Formula: see text], it is assumed that [Formula: see text] is unramified over [Formula: see text]. Moreover, some interesting identities for exponential sums are proved.

Quadratic-Congruence Carrier-Hopping Prime Code for Multicode-Keying Optical CDMA

2007 ◽  
Author(s):  
Wing C. Kwong ◽  
Cheng-Yuan Chang ◽  
Hung-Ta Chen ◽  
Guu-Chang Yang
Keyword(s):  
Optical Cdma ◽  
Quadratic Congruence
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