3.15. Use the Miller-Rabin test on each of the following numbers. In each case, either provide a Miller-Rabin witness for the compositeness of n, or conclude that n is probably prime by providing 10 numbers that are not Miller-Rabin witnesses for n. n (c) n = 294439 (a) n = 1105. (Yes, 5 divides n, but this is just a warm-up exercise!) (b) n = 294409 (d) n = 118901509 (f) n = 118901527 (e) n = 118901521 118915387 Solution to Exercise 3.15. (a) n − 1 = 1104 = 24. 69. 60 = n = 269 = -138 (mod 1105) (mod 1105) (mod 1105) (mod 1105) Thus 1105 is composite. It factors as n = 5.13.17. 22.69 = 259 24-69-324 28-69 1
3.15. Use the Miller-Rabin test on each of the following numbers. In each case, either provide a Miller-Rabin witness for the compositeness of n, or conclude that n is probably prime by providing 10 numbers that are not Miller-Rabin witnesses for n. n (c) n = 294439 (a) n = 1105. (Yes, 5 divides n, but this is just a warm-up exercise!) (b) n = 294409 (d) n = 118901509 (f) n = 118901527 (e) n = 118901521 118915387 Solution to Exercise 3.15. (a) n − 1 = 1104 = 24. 69. 60 = n = 269 = -138 (mod 1105) (mod 1105) (mod 1105) (mod 1105) Thus 1105 is composite. It factors as n = 5.13.17. 22.69 = 259 24-69-324 28-69 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
[Algebraic Cryptography] How do you solve this? Second picture is an example answer
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,