I am trying to find 1000-element of these linear recurrent sequences:
$1.$ $x_{i+5}=2x_{i+4}+5x_{i+3}+3x_{i+2}+4x_i$ if $x_{0,1,2,3,4}=(0,1,2,3,4)$. And we work over $GF(7)$.
$2.$ $y_{i+2}=2y_{i+1}-y_i+1$ if $y_{0,1} = (0,1)$. And we work over the field of complex numbers $C$.
Could you describe the approaches to solving these problems? Please write in detail!