Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 31, Problem 4P

a.

Program Plan Intro

To show that there are exactly (p1)2 quadratic residues, modulo p .

b.

Program Plan Intro

To give the efficient algorithm that determines whether a given number a is a quadratic residue modulo p . Analyze the efficiency of algorithm.

c.

Program Plan Intro

To prove that a is a quadratic residue in Z*p , then ak+1modp is a square root of a , modulo p if p is a prime of the form Introduction to Algorithms, Chapter 31, Problem 4P

d.

Program Plan Intro

To describe an efficient randomized algorithm for finding a nonquadratic residue and also find the number of arithmetic operations that algorithm will require on an average.

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