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Find all of the primitive roots of p53 (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 are all of the primitive roots of n, enter 91, 92, 9 ..., 9m 91 +92 ++ Im below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 8). • 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) (p-1)/2 (mod 7). Type your answer... x Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 67240, determine the total number of primitive roots modulo n. Type your answer...

Find all of the primitive roots of p53 (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 are all of the primitive roots of n, enter 91, 92, 9 ..., 9m 91 +92 ++ Im below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 8). • 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) (p-1)/2 (mod 7). Type your answer... x Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 67240, 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
Section1.1: Real Numbers
Problem 38E
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Need help with these two Intro to Elementary Number Theory Homework Problems.

 

Find all of the primitive roots of p53 (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 are all of the primitive roots of n, enter 91, 92, 9 ..., 9m 91 +92 ++ Im below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 8). • 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) (p-1)/2 (mod 7). Type your answer...
Transcribed Image Text:Find all of the primitive roots of p53 (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 are all of the primitive roots of n, enter 91, 92, 9 ..., 9m 91 +92 ++ Im below. Hints: • 2 is not a primitive root of any prime p > 3 such that p = 1,7 (mod 8). • 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) (p-1)/2 (mod 7). Type your answer...
x Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 67240, determine the total number of primitive roots modulo n. Type your answer...
Transcribed Image Text:x Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 67240, determine the total number of primitive roots modulo n. Type your answer...
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