quadratie residuosity problem - meaning and definition. What is quadratie residuosity problem
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What (who) is quadratie residuosity problem - definition

Quadratic residuacity problem; Quadratic residuocity problem; Quadratic Residuosity Problem

Quadratic residuosity problem         
The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers a and N, whether a is a quadratic residue modulo N or not.
Knapsack problem         
  • multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)
  • A demonstration of the dynamic programming approach.
PROBLEM IN COMBINATORIAL OPTIMIZATION
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
0/1 knapsack problem         
  • multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)
  • A demonstration of the dynamic programming approach.
PROBLEM IN COMBINATORIAL OPTIMIZATION
0/1 knapsack problem; 0-1 knapsack problem; Unbounded knapsack problem; Unbounded Knapsack Problem; Binary knapsack problem; Napsack problem; Backpack problem; 0-1 Knapsack problem; Integer knapsack problem; Knapsack Problem; Algorithms for solving knapsack problems; Methods for solving knapsack problems; Approximation algorithms for the knapsack problem; Bounded knapsack problem; Multiple knapsack problem; Rucksack problem; Computational complexity of the knapsack problem
<application> The knapsack problem restricted so that the number of each item is zero or one. (1995-03-13)

Wikipedia

Quadratic residuosity problem

The quadratic residuosity problem (QRP) in computational number theory is to decide, given integers a {\displaystyle a} and N {\displaystyle N} , whether a {\displaystyle a} is a quadratic residue modulo N {\displaystyle N} or not. Here N = p 1 p 2 {\displaystyle N=p_{1}p_{2}} for two unknown primes p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} , and a {\displaystyle a} is among the numbers which are not obviously quadratic non-residues (see below).

The problem was first described by Gauss in his Disquisitiones Arithmeticae in 1801. This problem is believed to be computationally difficult. Several cryptographic methods rely on its hardness, see § Applications.

An efficient algorithm for the quadratic residuosity problem immediately implies efficient algorithms for other number theoretic problems, such as deciding whether a composite N {\displaystyle N} of unknown factorization is the product of 2 or 3 primes.