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4. a) [15pts] Prove by induction that (fib(n)fib(n+1))=(0111)n(01) b) [5pts] Briefly describe how the formula in part a) can be employed to design an algorithm

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4. a) [15pts] Prove by induction that (fib(n)fib(n+1))=(0111)n(01) b) [5pts] Briefly describe how the formula in part a) can be employed to design an algorithm for computing fib(n) using O(logn) multiplications

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