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Let p be a prime.a. Determine the number of irreducible
Chapter 17, Problem 18E(choose chapter or problem)
QUESTION:
Problem 18E
Let p be a prime.
a. Determine the number of irreducible polynomials over Zp of the form x2 + ax + b.
b. Determine the number of irreducible quadratic polynomials over Zp.
Questions & Answers
QUESTION:
Problem 18E
Let p be a prime.
a. Determine the number of irreducible polynomials over Zp of the form x2 + ax + b.
b. Determine the number of irreducible quadratic polynomials over Zp.
ANSWER:
Step 1 of 3
Recall that the number of elements in are .
Note that and can be chosen in p ways each. Hence, these can be chosen in ways.
a)
Suppose is reducible. Then it can be factorized in the following way: