Prove Theorem 2.9: Let {P,..., Pk} and {9,...,9m} be nonrepeating lists of primes. Suppose that n...

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Prove Theorem 2.9: Let {P₁,..., Pk} and {9₁,...,9m} be nonrepeating lists of primes. Suppose that n is a natural number and both equations Tk n = =p²¹ Pk and n =q²₁².9 hold. Show that these product expressions are the same, up to reordering the factors. For example, p₁ could be 93, and then r₁ would necessarily be equal to t3. Prove Theorem 2.9: Let {P₁,..., Pk} and {9₁,...,9m} be nonrepeating lists of primes. Suppose that n is a natural number and both equations Tk n = =p²¹ Pk and n =q²₁².9 hold. Show that these product expressions are the same, up to reordering the factors. For example, p₁ could be 93, and then r₁ would necessarily be equal to t3.

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We have and Now nbr bru tm nq 9 divides n t ati qtm Im are primes ... View the full answer