1. (a) Find integers r and y such that 17r + 101y = 1. (b) Find 17-1 (mod 101). 2. (a) Solve 7d = 1 (mod 30). (b) Suppose you write a message as a number тт (тod 31). Encrypt m as m' (mod 31). Нow would you decrypt? (Нint: Decryption is done by raising the ciphertext to a power mod 31. Fermat's theorem will be useful.) 3. (a) Find all solutions of 12z = 28 (mod 236). (b) Find all solutions of 12r = 30 (mod 236). 4. (a) Use the Euclidean algorithm to compute ged(30030, 257). (b) Using the result of part (a) and the fact that 30030 = 2 · 3 · 5. 7· 11· 13, show that 257 is prime. (Remark: This method of computing one gcd, rather than doing several trial divisions (by 2, 3, 5, ...), is often faster for checking whet her small primes divide a number.)
1. (a) Find integers r and y such that 17r + 101y = 1. (b) Find 17-1 (mod 101). 2. (a) Solve 7d = 1 (mod 30). (b) Suppose you write a message as a number тт (тod 31). Encrypt m as m' (mod 31). Нow would you decrypt? (Нint: Decryption is done by raising the ciphertext to a power mod 31. Fermat's theorem will be useful.) 3. (a) Find all solutions of 12z = 28 (mod 236). (b) Find all solutions of 12r = 30 (mod 236). 4. (a) Use the Euclidean algorithm to compute ged(30030, 257). (b) Using the result of part (a) and the fact that 30030 = 2 · 3 · 5. 7· 11· 13, show that 257 is prime. (Remark: This method of computing one gcd, rather than doing several trial divisions (by 2, 3, 5, ...), is often faster for checking whet her small primes divide a number.)
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
please do it ASAP
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 5 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.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,