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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.

 

4. List all zero-divisors in Z20: Can you see a relationship between the
zero-divisors of Z, and the units of Zm
n?
20
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4. List all zero-divisors in Z20: Can you see a relationship between the zero-divisors of Z, and the units of Zm n? 20

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Expert Answer

Step 1

Zero divisors in a ring Z is an element a (non zero element), such that ab=0 where b is a non zero element of ring Z.

The unit divisor in a ring Z is an element a, such that ab=1 where b element of ring Z.

Step 2

Determine the set Z20.

Z20={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19}        

Step 3

Determine the elements of zero divisors.

Advanced Math homework question answer, step 3, image 1

So, zero divisors are {2,4,5,6,8,10,12,14,15,16,18}

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