Question: Discrete Maths (a) Give an inductive proof that the Fibonacci numbers Fm and Fm+1 are relatively prime for all m 2 0. The Fibonacci numbers

Discrete Maths

(a) Give an inductive proof that the Fibonacci numbers Fm and Fm+1 are relatively prime for all m 2 0. The Fibonacci numbers are defined as follows: Fo = 0 F1 = 1 Fm = Fm-1 + Fm-2 (for m > 2) (b) Give a recursive definition of the sequence {dk), k = 1, 2, . . . if (a) dk = 4k - 2; (b) dk = 1 + (-1)k; (c) dk = k(k + 1); (d) dk = k2

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