Question 1175673
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Hello,


full solution of this problem requires a lot of writing,  so I will not do it.



Instead,  I will refer to this source


http://jwilson.coe.uga.edu/EMAT6680Fa2014/Gieseking/Final%20Project/Fibonacci%20Numbers.html



You will find there a lot of interesting information about Fibonacci numbers,  and,  in particular, 

will find the answer to your current question.