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a. Let F, denote the n-th Fibonacci number. Using induction on n, prove that, for all n 21, we have Fn+2 2F. (A question that doesnt have to be turned in: What result involving the Euclidean algorithm does that remind you of?) b. Using the Euclidean algorithm, compute ged(13,8). (For the later parts of this question, c. How many iterations of the division algorithm did it take to compute ged (13, 8) in the previ- d. Compute ged(354224848179261915075, 218922995834555169026). Prove your answer us- notice that 13 is the 7th Fibonacci number and 8 is the 6th Fibonacci number.) ous part? ing induction. (You probably want to prove the next question at the same time. You may use without proof that 354224848179261915075 is the 100th Fibonacci number and 218922995834555169026 is the 99th Fibonacci number.) e. How many iterations of the division algorithm will it take to compute ged (354224848179261915075, 218922995834555169026)? Prove your answer using induction.
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