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Show that x4 + 1 is reducible over Zp for every prime p.

Chapter 17, Problem 29E

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QUESTION:

Show that x4 + 1 is reducible over Zp for every prime p. (This exercise is referred to in this chapter.)

Questions & Answers

QUESTION:

Show that x4 + 1 is reducible over Zp for every prime p. (This exercise is referred to in this chapter.)

ANSWER:

Step 1 of 8

Consider the polynomial

        

Need to prove  is reducible over.

To prove this, first claim the statement,

”In , whereis an odd prime, there exists such that

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