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Suppose that x is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 23548, determine the total number of primitive roots modulo n.

Suppose that x is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 23548, determine the total number of primitive roots modulo n.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Intro to Elementary Number Theory Homework Problems.

 

Suppose that is a primitive root modulo n, where n > 1 is an odd integer. If (n) = 23548, 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) = 23548, determine the total number of primitive roots modulo n. Type your answer...
Find all of the primitive roots of p = 89 (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 below. Hints: 91 +92 + +9m • 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)(-1)/2 (mod 7). Type your answer...
Transcribed Image Text:Find all of the primitive roots of p = 89 (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 below. Hints: 91 +92 + +9m • 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)(-1)/2 (mod 7). Type your answer...
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