Let n > 1 be an integer. We say that [x] ∈ℤ/n is a zero divisor if there exists [y] ∈ ℤ/n − {[0]} such that [x][y] = [0]. We say that [x] is a unit if there exists [y] ∈ 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?

Let n > 1 be an integer. We say that [x] ∈ℤ/n is a zero divisor if there exists [y] ∈ ℤ/n − {[0]} such that [x][y] = [0]. We say that [x] is a unit if there exists [y] ∈ 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?

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.1: Postulates For The Integers (optional)

Problem 25E: 25. Prove that if and are integers and, then either or. (Hint: If, then either or, and similarly...

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