The Fibonacci numbers fi, f2, f3,... are defined by setting fi= f2 = 1 and fn = fn-1+ fn-2 for all integers n ≥ 3. (a) Prove that for all integers n ≥ 3, gcd(fn, fn-1) = gcd(fn-1, fn-2). (b) Prove by induction on n that ged(fn, fn-1) = 1 for all integers n ≥ 2. 11 (c) Prove by induction on n that f = fn+1fn for all integers n ≥ 1.

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