If the integer n > 1 has the prime factorization , use Problem 3 to establish the following:
(a) ∑d|nµ(d)τ(d)=(− 1)r.
(b) ∑d|nµ(d)σ(d) = (− 1)rp1p2 ⋯ pr.
(c) ∑d|nµ(d)/d = (1 − 1/p1)(1 − 1/p2)⋯(1 − 1/pr).
(d) ∑d|ndµ(d)= (1 − 1/p1)(1 − 1/p2)⋯(1 − 1/pr).
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