## Even Fibonacci Numbers 2

Arithmetic, algebra, number theory, sequence and series, analysis, ...
square1001
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### Even Fibonacci Numbers 2

Let's consider about "Fibonacci Numbers". It looks like Problem 2, but it's difficult more than Problem 2.

Let $F_n = \begin{cases} 1 & n=0 \\ 2 & n=1 \\ F_{n-1}+F_{n-2} & n \ge 2 \end{cases}$

So, the sequence $F_i = 1,2,3,5,8,13,21,34,55,89,144,233,...$

By considering the terms in the Fibonacci sequence whose values do not exceed $10^{10^{13}}$, find the sum of the even-valued terms modulo $10^9+7$.

gbroxey
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Joined: Wed Mar 02, 2016 2:37 am