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# hw0(1) - CS 373 Combinatorial Algorithms Fall 2000 Homework...

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CS 373 Homework 0 (due 8/31/00) Fall 2000 2. (a) Prove that any positive integer can be written as the sum of distinct powers of 2 . For example: 42 = 2 5 + 2 3 + 2 1 , 25 = 2 4 + 2 3 + 2 0 , 17 = 2 4 + 2 0 . [Hint: “Write the number in binary” is not a proof; it just restates the problem.] (b) Prove that any positive integer can be written as the sum of distinct nonconsecutive Fi- bonacci numbers—if F n appears in the sum, then neither F n +1 nor F n 1 will. For exam- ple: 42 = F 9 + F 6 , 25 = F 8 + F 4 + F 2 , 17 = F 7 + F 4 + F 2 .
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hw0(1) - CS 373 Combinatorial Algorithms Fall 2000 Homework...

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