Answered: 3) An element of a ring is said to be…

3) An element of a ring is said to be idempotent if it satisfies x2 = x. Find all idempotent elements of Z/20Z. HINT: This is equivalent to finding all solutions to the congruence x2 = x mod 20.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 33E: 33. An element of a ring is called nilpotent if for some positive integer . Show that the set of all...

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Question

Please show this using

x^2 - x = x(x-1) equiv 0 mod 20

with x or x-1 being a multiple of 5(or 4)

3) An element of a ring is said to be idempotent if it satisfies x2 = x. Find all idempotent
elements of Z/20Z.
HINT: This is equivalent to finding all solutions to the congruence x2 = x mod 20.

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