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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 are all of the primitive roots of n, enter 91, 92, 9m .... 91929m 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) (p-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).

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 are all of the primitive roots of n, enter 91, 92, 9m .... 91929m 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) (p-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).

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 Problem.

 

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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