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).
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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