Purchase Solution

# Irreducible Polynomials

Not what you're looking for?

Show that there are exactly (p^2-p)/2 monic irreducible polynomials of degree 2 over Z_p, where p is any prime.

Using the definition of irreducibility, Theorem: A polynomial of degree 2 or 3 is irreducible over the field F iff it has no roots in F, or Lemma of Theorem: The nonconstant polynomial p(x) an element of F[x] is irreducible over F iff for all f(x), g(x) an element of F[x], p(x)|(f(x)g(x)) implies p(x)|f(x) or p(x)|g(x), or any other known theorems of polynomials except those involving irreducibility.

##### Solution Summary

This solution is comprised of a detailed explanation to show that there are exactly (p^2-p)/2 monic irreducible polynomials of degree 2 over Z_p, where p is any prime.

##### Solution Preview

suppose that X^2 + aX + b is irreducible over Z_p. so there are p^2 possibilities for the ...

##### Free BrainMass Quizzes

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts