Prove Theorem 2.9: Let {P,..., Pk} and {9,...,9m} be nonrepeating lists of primes. Suppose that n is a natural number and both equations Tk n = =p Pk and n =q.9 hold. Show that these product expressions are the same, up to reordering the factors. For example, p could be 93, and then r would necessarily be equal to t3.