Suppose p is a prime of at least 3 digits (i.e. P > 100). For each of the following q (related to p), under what conditions (if any) is 2 is a primitive root of q? Provide a brief justification in your own words. (a) q = 2p +1 and q is prime. (b) q = 4p +1 and q is prime. (c) q = 8p +1 and q is prime.
Suppose p is a prime of at least 3 digits (i.e. P > 100). For each of the following q (related to p), under what conditions (if any) is 2 is a primitive root of q? Provide a brief justification in your own words. (a) q = 2p +1 and q is prime. (b) q = 4p +1 and q is prime. (c) q = 8p +1 and q is prime.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.2: Mathematical Induction
Problem 49E: Show that if the statement
is assumed to be true for , then it can be proved to be true for . Is...
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Transcribed Image Text:Suppose p is a prime of at least 3 digits (i.e. p > 100). For each of the following q (related to p), under what
conditions (if any) is 2 is a primitive root of q? Provide a brief justification in your own words.
(a) q = 2p+1 and q is prime.
(b) q = 4p +1 and q is prime.
(c) q = 8p+1 and q is prime.
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