scholarly journals Reformulation of a Special Standard Quadratic Congruence of Even Composite Modulus

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
B. M. Roy
Keyword(s):  
Special Standard ◽  
Composite Modulus ◽  
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.

scholarly journals RP-181: Formulation of Standard Quadratic Congruence of Even Composite Modulus modulo an Even Prime Raised to the Power n

2021 ◽  
Vol 9 (8) ◽  
pp. 3064-3069
Author(s):  
Prof B M Roy
Keyword(s):  
Number Theory ◽  
Positive Integer ◽  
Complete Formulation ◽  
Composite Modulus ◽  
Quadratic Congruence ◽  
Keywords Composite

Abstract: The paper presented here, is a standard quadratic congruence of composite modulus, studied rigorously and found the formulation incomplete. It was partially formulated by the earlier mathematicians. The present authors realised that the earlier formulation need a completion and a reformulation of the solutions is done along with two more results. The author considered the problem for reformulation, studied and reformulated the solutions completely. A partial formulation is found in a books of Number Theory by Zuckerman at el. There the formulation is only for an odd positive integer but nothing is said about even positive integer. The authors have provided a complete formulation of the said quadratic congruence and presented here. Keywords: Composite Modulus, Quadratic Congruence, Reformulation.

National primary special standard for the unit of polarization mode dispersion in optical fiber

2012 ◽  
Vol 55 (2) ◽  
pp. 109-114
Author(s):  
V. V. Grigoriev ◽  
V. E. Kravtsov ◽  
A. K. Mityurev ◽  
A. B. Pnev ◽  
S. V. Tikhomirov
Keyword(s):  
Optical Fiber ◽  
Polarization Mode Dispersion ◽  
Polarization Mode ◽  
Special Standard ◽  
Mode Dispersion

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
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