a) Show that if a, b, and c are integers with (a, b) = (a, c) = 1, then (a, be) = 1.
b) Use mathematical induction to show that if a1, a2, …, an are integers, and b is another integer such that (a1, b) = (a2, b) = ⋯ = (an, b) = 1, then (a1a2 ⋯ an, b) = 1.
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