Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
4. Show that if a²p 1 a² - 1 where a > 1 is an integer and p is an odd prime with pła(a²- 1), n then n is a pseudoprime base a. Hint: First show that 2p | (n − 1). Then consider an−¹ – 1. Note that this shows that there are infinitely many pseudoprimes base a for any a.

4. Show that if a²p 1 a² - 1 where a > 1 is an integer and p is an odd prime with pła(a²- 1), n then n is a pseudoprime base a. Hint: First show that 2p | (n − 1). Then consider an−¹ – 1. Note that this shows that there are infinitely many pseudoprimes base a for any a.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

[Number Theory] How do you solve question 4? thanks 

1. Show that 25 is a strong pseudoprime base 7, i.e., passes Miller's test base 7. 2. Use the method of squaring to compute 51711 mod 1911. 3. (i) For a prime p suppose that n = 2² - 1 is not a prime. Show that n is a pseudoprime base 2. (ii) Show every composite Fermat number Fm 4. Show that if = n 22m + 1 is a pseudoprime base 2. a²p 1 a² - 1 where a > 1 is an integer and p is an odd prime with pła(a²-1), then n is a pseudoprime base a. Hint: First show that 2p | (n − 1). Then consider an−¹ – 1. Note that this shows that there are infinitely many pseudoprimes base a for any a.
Transcribed Image Text:1. Show that 25 is a strong pseudoprime base 7, i.e., passes Miller's test base 7. 2. Use the method of squaring to compute 51711 mod 1911. 3. (i) For a prime p suppose that n = 2² - 1 is not a prime. Show that n is a pseudoprime base 2. (ii) Show every composite Fermat number Fm 4. Show that if = n 22m + 1 is a pseudoprime base 2. a²p 1 a² - 1 where a > 1 is an integer and p is an odd prime with pła(a²-1), then n is a pseudoprime base a. Hint: First show that 2p | (n − 1). Then consider an−¹ – 1. Note that this shows that there are infinitely many pseudoprimes base a for any a.
Expert Solution
steps

Step by step

Solved in 3 steps with 74 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS