Let f (x), g(x) ∈ F [x]. (a) Show that if f (x)|g(x) and g(x)|f (x), then there is some c ∈ F so that f (x) = c · g(x). In this case, f (x) and g(x) are called associates. (b) Show that if f (x) and g(x) are monic, then in fact f (x) = g(x). (c) Prove the converse of part (a). That is, that f (x) and g(x) are associates if and only if f (x)|g(x) and g(x)|f (x).

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