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# Nilpotent Elements - Divisibility by Every Prime

ABSALG-G1YXER

An element $x$ of ring $R$ is called nilpotent if $x^n = 0$ for some integer $n$. In the ring $\mathbb{Z}/m\mathbb{Z}$, $x$ is nilpotent if and only if $x$ is divisible by every prime factor of $m$.

Which elements of $\mathbb{Z}/12\mathbb{Z}$ are nilpotent?

Select ALL that apply.

A

$0$

B

$2$

C

$4$

D

$6$

E

$10$