You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 58E: a. Prove that 10n(1)n(mod11) for every positive integer n. b. Prove that a positive integer z is...
icon
Related questions
Question
please send solution handwritten solution asap
You and your friend Lara are considering the linear congruence
ax = b (mod m),
where
m = 6 x 11 x 233,
b = 232 x 379
and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and
379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question.
(a) Lara askes you to give all a in the range 2645 < a < 2665 for which the linear congruence ax = b (mod m)
has a unique solution modulo m. Enter your answer in the box below and make sure you follow the syntax advice.
Answer: the linear congruence has a unique solution for a in the set
Transcribed Image Text:You and your friend Lara are considering the linear congruence ax = b (mod m), where m = 6 x 11 x 233, b = 232 x 379 and a is an unspecified integer in the range 2645 < a < 2665. In this question you may assume that 11, 23 and 379 are prime numbers, and you may use the table of prime factorisations given at the bottom of the question. (a) Lara askes you to give all a in the range 2645 < a < 2665 for which the linear congruence ax = b (mod m) has a unique solution modulo m. Enter your answer in the box below and make sure you follow the syntax advice. Answer: the linear congruence has a unique solution for a in the set
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Basics (types, similarity, etc)
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
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Algebra: Structure And Method, Book 1
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