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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
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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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).]
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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