Find all solutions to the equation [50]114 Y = [8]114 for Y EZ114. Justify your answer.
Find all solutions to the equation [50]114 Y = [8]114 for Y EZ114. Justify your answer.
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.5: Multiplication With The Addition-or-subtraction Method
Problem 31P
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Question
Can yuo please help with, part b, thank you.
![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%2F4082be17-8615-459e-878a-685f4f1bd2cd%2Ffca16a5a-17d2-4921-812d-c7551aeaac05%2Fb2o7m0d_processed.jpeg&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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