Let P(n) be a property involving a natural number n. Suppose that we know that P(n) implies P(n – 1) for any n> 1. Suppose we also know that P(n) implies P(2n) for any n > 1. Finally, suppose that we know that P(1) holds. Show that P(n) holds for every n > 1. (This is sometimes known as the principle of forwards-backwards induction.

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