## Problem of the Day #189: Fibonacci DoublingSeptember 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.