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Consider the following two polynomials in F17[x]
(a) Use Karatsuba's algorithm, by hand, to multiply these two polynomials.
(b) Use the FFT algorithm, by hand, to multiply these two polynomials.
Remember that if a polynomial has degree 3 or less then it is irreducible if and only if it has at least one linear factor, that (x - a) is a linear factor of a polynomial f(x) if and only if f(a) = 0 and that for small elds it is easy to check by hand if a particular value is a root of a polynomial.
(a) Which of the following polynomials are reducible and irreducible in F5[x]? What is the factorization of the reducible ones?
(b) Does the following system have a unique solution of smallest degree:
Let R be the relation on the set of ordered pairs of positive integers such that ((a, b), (c, d)) ∈ R if and only if ad = bc. Determine whether R is an equivalence relation or a p
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Multiplication of complex numbers: Example 1: Combine the subsequent complex numbers: (4 + 3i) + (8 - 2i) - (7 + 3i) = Solution: (4 + 3i) + (8 - 2i) - (7 + 3i
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0+50x1-60-60x0+10
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