Let n = pk1 1 pk2 2 pkm m where p1, p2,..., pm are distinct prime numbers and k1
Chapter 9, Problem 30(choose chapter or problem)
Let \(n = p^{k1}_{1} p^{k2}_{2}· · · p^{km}_{m}\) where \(p_{1}, p_{2}, . . . , p_{m}\) are distinct prime numbers and \(k_{1}, k_{2}, . . . , k_{m}\) are positive integers. How many ways can n be written as a product of two positive integers that have no common factors
a. assuming that order matters (i.e., 8·15 and 15·8 are regarded as different)?
b. assuming that order does not matter (i.e., 8·15 and 15·8 are regarded as the same)?
Text Transcription:
n = p^k1_1 p^k2_2· · · p^km_m
p_1, p_2, . . . , p_m
k_1, k_2, . . . , k_m
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