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)