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Prove that if p is a prime, then the field Zp is not algebraically closed

Chapter 32, Problem 32.6

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QUESTION:

Prove that if p is a prime, then the field Zp is not algebraically closed.

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QUESTION:

Prove that if p is a prime, then the field Zp is not algebraically closed.

ANSWER:

Step 1 of 2

Suppose F is a finite field with n elements. Then the field F can be defined as:

 

Construct a polynomial  

The polynomial will never be zero in the field . There exists a polynomial which has no zero in the field

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