Selected Answers to Problem Set 12

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Since @(pq) = (p-1)(q-1) and n = pq = 39,233,944, then:

            (p-1)(q-1) = 39,233,944
        pq - p - q + 1 = 39,233,944
39,247,771 - p - q + 1 = 39,233,944
            -p - q + 1 = -13827
                -p - q = -13828
                 p + q = 13828

And since pq = 39,247,771, q = 39,247,771 / p:

p + (39247771 / p) = 13828

p2 + 39,247,771 - 13828p = 0

p = {9839, 3989}.  

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