$$y = (5+ 2\sqrt{6})^{1+2^x}$$
where $0 \leq x < 2^{32}$ and a prime number $p(p<46337)$,calculate $r = \floor{y} \;mod\; p$.

$$r = (5+ 2\sqrt{6})^{1+2^x} + (5 - 2\sqrt{6})^{1+2^x} -1$$

$$a_0=2,a_1=10,a_n = a_{n-1} +a_{n-2}$$

$$(a_{1+2^n} - 1) \;mod\; M$$

$$\left( \begin{matrix} a_{n} \\ a_{n-1} \end{matrix} \right) = A \left( \begin{matrix} a_{n-1} \\ a_{n-2} \end{matrix} \right) = A^{n-1} \left( \begin{matrix} a_1 \\ a_0 \end{matrix} \right)$$

$$\left( \begin{matrix} r \\ * \end{matrix} \right) = A^{2^x} \left( \begin{matrix} 10 \\ 2 \end{matrix} \right)$$

$$|GL(n,p)| = \prod_{i=0}^{n-1} (p^n-p^i)$$