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Asked Feb 9, 2020
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Can someone please help me understand the following problem. I need to know how to start the problem. i need to know the theorems ,identities,  used please thank you.

 

20. Show that Z. has a nonzero nilpotent element if and only if n is di-
visible by the square of some prime.
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20. Show that Z. has a nonzero nilpotent element if and only if n is di- visible by the square of some prime.

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Expert Answer

Step 1

Given: n is divisible by the square of prime.

To prove: Zn has a non zero nilpotent element.

Step 2

Assume the prime number, p

So,

n=p2t

For the element a=pt

(pt)2=p2t2

        =nt

   &...

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Advanced Math