scholarly journals Structures of power digraphs over the congruence equation $ x^p\equiv y\; (\text{mod}\; m) $ and enumerations

2021 ◽  
Vol 6 (5) ◽  
pp. 4581-4596
Author(s):  
M. Haris Mateen ◽  
◽  
Muhammad Khalid Mahmmod ◽  
Dilshad Alghazzawi ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Congruence Equation

Enhanced Rabin cryptosystem based on cubic congruence equation

2009 ◽  
Vol 29 (7) ◽  
pp. 1803-1805
Author(s):  
Tian-xiang ZHENG
Keyword(s):  
Congruence Equation

On a congruence equation and related arithmetical identities

1967 ◽  
Vol 71 (1) ◽  
pp. 24-31 ◽  
Author(s):  
K. Nageswara Rao
Keyword(s):  
Congruence Equation

scholarly journals A MEAN VALUE RELATED TO D. H. LEHMER'S PROBLEM AND THE RAMANUJAN'S SUM

2011 ◽  
Vol 54 (1) ◽  
pp. 155-162 ◽  
Author(s):  
ZHANG WENPENG
Keyword(s):  
Mean Value ◽  
Mean Value Theorem ◽  
Opposite Parity ◽  
Fixed Integer ◽  
All Solutions ◽  
The Mean ◽  
Ramanujan’S Sum ◽  
Lehmer’S Problem ◽  
Congruence Equation ◽  
Ramanujan's Sum

AbstractLet q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with 1 ≤ a ≤ q − 1, it is clear that there exists one and only one b with 0 ≤ b ≤ q − 1 such that ab ≡ c (mod q). Let N(c, q) denotes the number of all solutions of the congruence equation ab ≡ c (mod q) for 1 ≤ a, b ≤ q − 1 in which a and b are of opposite parity, where b is defined by the congruence equation bb ≡ 1(modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving (N(c, q) − φ(q)) and Ramanujan's sum, and give two exact computational formulae.

Greyscale-images-oriented progressive secret sharing based on the linear congruence equation

2017 ◽  
Vol 77 (16) ◽  
pp. 20569-20596 ◽  
Author(s):  
Lintao Liu ◽  
Yuliang Lu ◽  
Xuehu Yan ◽  
Huaixi Wang
Keyword(s):  
Secret Sharing ◽  
Linear Congruence ◽  
Progressive Secret Sharing ◽  
Congruence Equation

scholarly journals One kind power mean of the hybrid Gauss sums

2018 ◽  
Vol 16 (1) ◽  
pp. 531-538
Author(s):  
Qi Lan ◽  
Zhang Wenpeng
Keyword(s):  
Exact Formula ◽  
Gauss Sums ◽  
Computational Formula ◽  
Analysis Method ◽  
Power Mean ◽  
Trigonometric Sums ◽  
Number Of Solutions ◽  
Computational Problem ◽  
Congruence Equation

AbstractIn this paper, we use the analysis method and the properties of trigonometric sums to study the computational problem of one kind power mean of the hybrid Gauss sums. After establishing some relevant lemmas, we give an exact computational formula for it. As an application of our result, we give an exact formula for the number of solutions of one kind diagonal congruence equation modp, wherepbe an odd prime.

scholarly journals On 4-valent Frobenius circulant graphs

2012 ◽  
Vol Vol. 14 no. 2 (Graph Theory) ◽  
Author(s):  
Sanming Zhou
Keyword(s):  
Number Theory ◽  
Interconnection Networks ◽  
Prime Factor ◽  
Additive Group ◽  
Sense Making ◽  
Recursive Construction ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
International Audience ◽  
Congruence Equation

Graph Theory International audience A 4-valent first-kind Frobenius circulant graph is a connected Cayley graph DLn(1, h) = Cay(Zn, H) on the additive group of integers modulo n, where each prime factor of n is congruent to 1 modulo 4 and H = {[1], [h], −[1], −[h]} with h a solution to the congruence equation x 2 + 1 ≡ 0 (mod n). In [A. Thomson and S. Zhou, Frobenius circulant graphs of valency four, J. Austral. Math. Soc. 85 (2008), 269-282] it was proved that such graphs admit 'perfect ' routing and gossiping schemes in some sense, making them attractive candidates for modelling interconnection networks. In the present paper we prove that DLn(1, h) has the smallest possible broadcasting time, namely its diameter plus two, and we explicitly give an optimal broadcasting in DLn(1, h). Using number theory we prove that it is possible to recursively construct larger 4-valent first-kind Frobenius circulants from smaller ones, and we give a methodology for such a construction. These and existing results suggest that, among all 4-valent circulant graphs, 4-valent first-kind Frobenius circulants are extremely efficient in terms of routing, gossiping, broadcasting and recursive construction.

Radial GRIN Lenses based on the Solution of a Regularized Ray Congruence Equation

2021 ◽  
pp. 1-1
Author(s):  
Anastasios Paraskevopoulos ◽  
Francesca Maggiorelli ◽  
Matteo Albani ◽  
Stefano Maci
Keyword(s):  
Congruence Equation
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