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Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] E Z /n – {[0]} such that [x][y] = [0]. We say that [æ] is a unit if there exists [y] E Z /n such that [x][y] = [1]. 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)

Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] E Z /n – {[0]} such that [x][y] = [0]. We say that [æ] is a unit if there exists [y] E Z /n such that [x][y] = [1]. 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)

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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Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] e Z/n – {[0]} such that ["]Y) exists [y] E Z /n such that [x][y] = [1]. [0]. We say that [x] is a unit if there 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)
Transcribed Image Text:Let n > 1 be an integer. We say that [x] E Z/n is a zero divisor if there ex- ists [y] e Z/n – {[0]} such that ["]Y) exists [y] E Z /n such that [x][y] = [1]. [0]. We say that [x] is a unit if there 7a) What are all the units in Z/12? What are all the zero divisors? b) What are all the units in Z/14? What are all the zero divisors? c) What are all the units in Z/13? What are all the zero divisors? (You do not need to prove your answers to this question, but you should show your work.)
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