4. (i) For an odd number n, suppose that 2" #2 mod n. Can n be a prime? Explain. This is called the base 2 primality test. (ii) Using the fact that 187 = 11-17, show that 2186174 mod 187. This shows that 187 fails the base 2 primality test. (iii) Compute 2561 mod 561. Use Fermat's little theorem and hand calculations. Does 561 pass or fail the base 2 primality test? You may use the prime factorization of 561.
4. (i) For an odd number n, suppose that 2" #2 mod n. Can n be a prime? Explain. This is called the base 2 primality test. (ii) Using the fact that 187 = 11-17, show that 2186174 mod 187. This shows that 187 fails the base 2 primality test. (iii) Compute 2561 mod 561. Use Fermat's little theorem and hand calculations. Does 561 pass or fail the base 2 primality test? You may use the prime factorization of 561.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
Related questions
Question
[Number Theory] How do you solve question 4?
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 3 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
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