ON SOLUTIONS OF QUADRATIC CONGRUENCE USING GRAPHS

2019 ◽  
Vol 113 (1) ◽  
pp. 65-73
Author(s):  
LiMin Yang
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.

Distribution of the roots of a quadratic congruence

1992 ◽  
Vol 62 (4) ◽  
pp. 2936-2942
Author(s):  
O. M. Fomenko
Keyword(s):  
Quadratic Congruence

On the addition of two weighted squares of units mod n

2016 ◽  
Vol 12 (07) ◽  
pp. 1783-1790 ◽  
Author(s):  
Cui-Fang Sun ◽  
Zhi Cheng
Keyword(s):  
Positive Integer ◽  
Number Of Solutions ◽  
Residue Classes ◽  
Quadratic Congruence

For any positive integer [Formula: see text], let [Formula: see text] be the ring of residue classes modulo [Formula: see text] and [Formula: see text] be the group of its units. Recently, for any [Formula: see text], Yang and Tang obtained a formula for the number of solutions of the quadratic congruence [Formula: see text] with [Formula: see text] units, nonunits and mixed pairs, respectively. In this paper, for any [Formula: see text], we give a formula for the number of representations of [Formula: see text] as the sum of two weighted squares of units modulo [Formula: see text]. We resolve a problem recently posed by Yang and Tang.

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