Question: For m Z+ let Dm = {d Z+ | d divides m}. For d Dm let Sd = {n|0 < n

For m ∈ Z+ let Dm = {d ∈ Z+ | d divides m}. For d ∈ Dm let Sd = {n|0 < n ≤ m and gcd(n, m) = d}.
(a) Show that the collection Sd, d ∈ Dm, provides a partition of {1, 2, 3, 4,..., m - 1, m}.
(b) Determine |Sd| for each d ∈ Dm.

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