Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Algebra: Structure And Method, Book 1
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
See similar textbooks
icon
Related questions
Question

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...
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS