## Problem of the Day #189: Fibonacci Doubling
*September 24, 2011*

*Posted by Albert in : potd , trackback*

Find the value of:

$$\sum\limits_{n=1}^{10^{12}} F_{2n} \pmod{1,000,003}$$

Where $F_n$ is the $n^{\text{th}}$ Fibonacci number, defined as:

$$

\begin{eqnarray}

F_0 & = & 0 \\

F_1 & = & 1 \\

F_n & = & F_{n-1} + F_{n-2}

\end{eqnarray}

$$

You may use a computational resource.

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