Prove that every positive integer n can be written as the sum of distinct powers of 2. E.g. 1 = 2º, 7 = 2² +2+1. Hint: use strong induction. You may use the fact that for all positive integer n, there exists a non-negative integer m such that 2m ≤ n < 2m+¹, i.e. 2m is the largest power of 2 no greater than n.

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