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Use strong induction to show that every positive integer n can be written as a sum of distinct powers of two, that is, asasumofasubsetoftheintegers2^0 =1,2^1 =2,2^2 =4, and so on. [Hint: For the inductive step, separately con- sider the case where k + 1 is even and where it is odd. When it is even, note that (k + 1)/2 is an integer.]

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