Show that Zn has a nonzero nilpotent element if and only if n is divisibleby the square of some prime.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 13E
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Show that Zn has a nonzero nilpotent element if and only if n is divisible
by the square of some prime.

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