scholarly journals ON SOLUTIONS TO SOME POLYNOMIAL CONGRUENCES IN SMALL BOXES

2013 ◽  
Vol 89 (2) ◽  
pp. 300-307
Author(s):  
IGOR E. SHPARLINSKI
Keyword(s):  
Exponential Sums ◽  
Polynomial Systems ◽  
Side Length ◽  
Character Sum ◽  
Number Of Solutions ◽  
Polynomial Congruences

AbstractWe use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solutions in boxes with the side length below ${p}^{1/ 2} $, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.

scholarly journals Recursive Elucidation of Polynomial Congruences Using Root-Finding Numerical Techniques

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
M. Khalid Mahmood ◽  
Farooq Ahmad
Keyword(s):  
Iterative Methods ◽  
Logarithmic Scale ◽  
Numerical Techniques ◽  
Root Finding ◽  
Polynomial Congruences ◽  
Polynomial Congruence

In this paper we put forward a family of algorithms for lifting solutions of a polynomial congruencemod pto polynomial congruencemod pk. For this purpose, root-finding iterative methods are employed for solving polynomial congruences of the formaxn≡b(mod pk),k≥1,wherea,b,andn>0are integers which are not divisible by an odd primep. It is shown that the algorithms suggested in this paper drastically reduce the complexity for such computations to a logarithmic scale. The efficacy of the proposed technique for solving negative exponent equations of the formax-n≡b(mod pk)has also been addressed.

scholarly journals On polynomial congruences

2016 ◽  
Vol 90 (6) ◽  
pp. 1115-1127
Author(s):  
Agata Lewicka
Keyword(s):  
Polynomial Congruences

Polynomial Congruences and Density

2007 ◽  
Vol 80 (4) ◽  
pp. 299-302
Author(s):  
Gerry Myerson
Keyword(s):  
Polynomial Congruences
Sign in / Sign up

Export Citation Format

Share Document