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The Lucas numbers are given by the recurrence Ln = Ln?1 + Ln?2 with boundary conditions L0 = 2, L1 = 1. (a) Show that

The Lucas numbers are given by the recurrence Ln = Ln?1 + Ln?2 with boundary conditions L0 = 2, L1 = 1.

(a) Show that Ln = fn?1 + fn+1 for n ? 2, where fn is the nth Fibonacci number.

(b) Find a closed form solution for the Lucas numbers

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