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Fibo meets Lucas #1 (Posted on 2018-09-09) Difficulty: 3 of 5
Keeping the Fibonacci rule of adding the latest two to get the next but starting from 2 and 1 (in this order) instead of 0 and 1 for the (ordinary Fibonacci numbers) one defines the series of Lucas Numbers:
L(n) = L(n-1) + L(n-2) for n>1
L(0) = 2
L(1) = 1
Here are some more values of L(n) together with the Fibonacci numbers
for comparison:
F(n):	0	1	1	2	3	5	8	13	21	34	55	...
L(n): 2 1 3 4 7 11 18 29 47 76 123 ...
With the above information in background prove the following formulas:

a. F(n-1)+ F(n+1) = L(n)
b. L(n-1) + L(n+1)= 5*F(n)
c. F(n)* L(n) = F(2n)

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( You must be logged in to post comments.)
  Subject Author Date
part c) soln. , using Binet' formulaeSteven Lord2018-09-09 16:03:53
a and b soln.sSteven Lord2018-09-09 09:52:01
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