(a) Given an n−bit integer number a = an−1an−2 . . . a0 define a polynomial A(x) satisfying A(2) = a. (b) Given two n−bit integers a and b, give an algorithm to multiply them in O(n log(n)) time. Use the FFT algorithm from class as a black-box (i.e. don’t rewrite the code, just say run FFT on ...). Explain your algorithm in words and analyze its running time. (Think/investigate why this is not enough to claim a fast multiplication algorithm).

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