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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.
Find all subfields of Q ( sqrt2, sqrt 3) with proof that you have them all. What is the minimal polynomial of sqrt2+ sqrt3? Which subfields does it generate over Q?
Eve said to Adam, "If you give me one dollar, then we will have the same amount of money." Adam then replied, "Eve, if you give me one dollar I will have double the amount of money you are left with." How much does each have?
Solve the recurrence relation a(n)=3a(n-1)+10a(n-2) with the initial conditions a(0)=0 and a(1)=2. Solve the recurrence relation a(n)=3a(n-1)+10a(n-2) +12 with the initial conditions a(0)=0 and a(1)=2.
the rectangular part of the field is 100 yards long and the diameter of each semicircle is 50 yards.find the cost of firtilizing the field at $0.30 per square yard.
Geometric Interpretation of the Subspace, Show that the set of all elements of R^2 of the form (a, -a), where a is any real number
What is Diane's current monthly mortgage payment? What is Diane's current outstanding principal?
The bucket is filled with 43 pounds of water and is pulled up at a rate of 2.8 feet per second, but water leaks out of a hole in the bucket at a rate of 0.15 pounds per second. Find the work done pulling the bucket to the top of the well. Your ans..
Suppose that a straight line is given by L(t) = (1+t, 2+t, 3-t), - ∞
Determine the number of points in the sample space of the possible arrangements of boys and girls.
Recall that in Theorem 1.1.3 we proved that O is the center of the circumscribed circle, that is, a circle containing the vertices A, B, and C of the triangle. Use the Two-Reflections Theorem to prove that the inscribed angle ABC is measured by ha..
eet over a horizontal distance of 456 feet. Find the slope of the path. Round your answer to two decimal places.
What did the doctor say after examining Yunn Yunsberger.
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