Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which ak 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45.
Make sure that all your answers are explained carefully. (a) Remember that the order k = ordma is the smallest positive integer for which ak 1 mod m. Determine the order of 11 modulo 21. (b) For each of the following positive integers, say whether it has a primitive root or not. Explain why. (i) a = 19, (ii) b = 250, (iii) d = 45.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 91E
Related questions
Question

Transcribed Image Text:Question 4
Make sure that all your answers are explained carefully.
(a) Remember that the order k = ordma is the smallest positive integer for which a = 1
mod m. Determine the order of 11 modulo 21.
(b) For each of the following positive integers, say whether it has a primitive root or not.
Explain why.
(i) a = 19,
(ii) b = 250,
(iii) d = 45.
1
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images

Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

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

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage

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

Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,


Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL