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13. Show that
14. Show that 
15. Evaluate 
16. Evaluate
(a) 
(b) 
17. Let F0, F1, F2,
... be the Fibonacci sequence.
(a) Show that 
(b) Find numbers x, y, and z such that F2n = xFn2 + yFnFn+1 + zFn+12.
(c) Find x, y, z, and w such that F3n = xFn3 + yFn2Fn+1 + zFnFn+12 + wFn+13.
(d) Find analogues of the formulas above for the Lucas
numbers.
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Wednesday, June 10, 1998