|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.
|State whether the following statements are true or false. Show working. a. For each odd prime p, a residue a in Z*p cannot be both a primitive root and a quadratic residue. b. The integer 2 has a quadratic residue modulo the prime 399989. c. If p, q are odd primes and pg = 1 mod 4, then -1 has a quadratic residue modulo at least one of p or q.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.8: Introduction To Cryptography (optional)
Problem 1TFE: Label each of the following statements as either true or false.
The notation mod is used to...
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