Solution Found!
Suppose that f(x)Zp[x] and f(x) is irreducible over Zp,
Chapter 17, Problem 8E(choose chapter or problem)
QUESTION:
Suppose that f(x)?Zp[x] and f(x) is irreducible over Zp, where p is a prime. If deg f(x) = n, prove that is a field with pn elements.
Questions & Answers
QUESTION:
Suppose that f(x)?Zp[x] and f(x) is irreducible over Zp, where p is a prime. If deg f(x) = n, prove that is a field with pn elements.
ANSWER:Step 1 of 3
Implies that is maximal ideal in , which implies that is a field.
Now we need to count the number of elements in this field.