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Find all of the primitive roots of p = 83 (recall that we defined primitive roots to be certain integers strictly between 0 and n). Enter the sum of all primitive roots, i.e., if 91,92,..., 9m are all of the primitive roots of n, enter 91 +92 + + 9m below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 4). • 3 is not a primitive root of any prime p > 5 such that p = (-1) (-1)/2 (mod 3). • 5 is not a primitive root of any prime p≥7 such that p = 1 (mod 5). • 7 is not a primitive root of any prime p > 11 such that p = (-1) (-1)/2 (mod 7). Type your answer... Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 49284, determine the total number of primitive roots modulo n. Type your answer...

Find all of the primitive roots of p = 83 (recall that we defined primitive roots to be certain integers strictly between 0 and n). Enter the sum of all primitive roots, i.e., if 91,92,..., 9m are all of the primitive roots of n, enter 91 +92 + + 9m below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 4). • 3 is not a primitive root of any prime p > 5 such that p = (-1) (-1)/2 (mod 3). • 5 is not a primitive root of any prime p≥7 such that p = 1 (mod 5). • 7 is not a primitive root of any prime p > 11 such that p = (-1) (-1)/2 (mod 7). Type your answer... Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 49284, determine the total number of primitive roots modulo n. Type your answer...

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 90E
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Need help with these two Intro to Elementary Number Theory Homework Problems.

 

Find all of the primitive roots of p = 83 (recall that we defined primitive roots to be certain integers strictly between 0 and n). Enter the sum of all primitive roots, i.e., if 91,92,..., 9m are all of the primitive roots of n, enter 91 +92 + + 9m below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 4). • 3 is not a primitive root of any prime p > 5 such that p = (-1) (-1)/2 (mod 3). • 5 is not a primitive root of any prime p≥7 such that p = 1 (mod 5). • 7 is not a primitive root of any prime p > 11 such that p = (-1) (-1)/2 (mod 7). Type your answer...
Transcribed Image Text:Find all of the primitive roots of p = 83 (recall that we defined primitive roots to be certain integers strictly between 0 and n). Enter the sum of all primitive roots, i.e., if 91,92,..., 9m are all of the primitive roots of n, enter 91 +92 + + 9m below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 4). • 3 is not a primitive root of any prime p > 5 such that p = (-1) (-1)/2 (mod 3). • 5 is not a primitive root of any prime p≥7 such that p = 1 (mod 5). • 7 is not a primitive root of any prime p > 11 such that p = (-1) (-1)/2 (mod 7). Type your answer...
Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 49284, determine the total number of primitive roots modulo n. Type your answer...
Transcribed Image Text:Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 49284, determine the total number of primitive roots modulo n. Type your answer...
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