3 (a) Using Euclid's algorithm, solve the equation [25]57 X = [4]57 for X € Z57. Show your working. [ (b) Find all solutions to the equation [50]114 · Y = [8]114 for Y E Z114. Justify your answer. [Hint: for part (b) you should notice that ([50]114)-¹ doesn't exist. Instead, write out what the equation means in terms of ordinary integers, and then relate it to part (a).]
3 (a) Using Euclid's algorithm, solve the equation [25]57 X = [4]57 for X € Z57. Show your working. [ (b) Find all solutions to the equation [50]114 · Y = [8]114 for Y E Z114. Justify your answer. [Hint: for part (b) you should notice that ([50]114)-¹ doesn't exist. Instead, write out what the equation means in terms of ordinary integers, and then relate it to part (a).]
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![3
(a) Using Euclid's algorithm, solve the equation [25] 57 X = [4]57 for X € Z57.
Show your working.
[
(b) Find all solutions to the equation [50]114 Y = [8]114 for Y € Z114. Justify your
●
answer.
[
[Hint: for part (b) you should notice that ([50]114)-¹ doesn't exist. Instead, write
out what the equation means in terms of ordinary integers, and then relate it to part (a).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc86229f7-e5a9-4e38-b872-4fc8db453ef1%2F89bba455-c855-4e22-a59b-7e24c166b6cc%2Fcub9o05_processed.png&w=3840&q=75)
Transcribed Image Text:3
(a) Using Euclid's algorithm, solve the equation [25] 57 X = [4]57 for X € Z57.
Show your working.
[
(b) Find all solutions to the equation [50]114 Y = [8]114 for Y € Z114. Justify your
●
answer.
[
[Hint: for part (b) you should notice that ([50]114)-¹ doesn't exist. Instead, write
out what the equation means in terms of ordinary integers, and then relate it to part (a).]
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