Prove Exercise 4.6.12 in the course notes. Then, assuming that gcd(a, n)|b, determine how many solutions (in Zm) the congruence ar = b (mod n) has. Explain your reasoning and provide examples to support your claim. (Hint: Look at Example 4.3.2.) 12. Prove that if gcd(a, n) † b, then ax = b (mod n) has no solutions.
Prove Exercise 4.6.12 in the course notes. Then, assuming that gcd(a, n)|b, determine how many solutions (in Zm) the congruence ar = b (mod n) has. Explain your reasoning and provide examples to support your claim. (Hint: Look at Example 4.3.2.) 12. Prove that if gcd(a, n) † b, then ax = b (mod n) has no solutions.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 60RE
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How do you prove this?
![Prove Exercise 4.6.12 in the course notes. Then, assuming that ged(a, n)|b, determine how many solutions
(in Z„) the congruence
ax = b (mod n)
has. Explain your reasoning and provide examples to support your claim.
(Hint: Look at Example 4.3.2.)
12. Prove that if gcd(a, n) † b, then ax = b (mod n) has no solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf4635d6-517f-4c42-9206-ddd0c06b9747%2Fcc4a69e0-df26-40bd-a6ff-ce0ee40d938d%2Fxwfh8r8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Prove Exercise 4.6.12 in the course notes. Then, assuming that ged(a, n)|b, determine how many solutions
(in Z„) the congruence
ax = b (mod n)
has. Explain your reasoning and provide examples to support your claim.
(Hint: Look at Example 4.3.2.)
12. Prove that if gcd(a, n) † b, then ax = b (mod n) has no solutions.
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