if x_0 =x_1 =1 and x_(n+1) =1996x_n +1997x_(n−1) for n≥2. Find the remainder of the division of x


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Question Number 90485 by Maclaurin Stickker last updated on 23/Apr/20

$i f x_{0} = x_{1} = 1 a n d x_{n + 1} = 1996 x_{n} + 1997 x_{n - 1}$ $f o r n ⩾ 2 . F i n d t h e r e m a i n d e r o f$ $t h e d i v i s i o n o f x_{1996} b y 3$
Commented by Maclaurin Stickker last updated on 23/Apr/20

$I f i n d t h e g e n e r a l t e r m o f s e q u e n c e$ $x_{n} = \frac{998 {(- 1)}^{n} + 1997^{n}}{999}$ $I f i t i s r i g h t, h o w c o u l d I f i n d t h e r e m a i n d e r$ $w i t h o u t {N e w t o n}^{'} s B i n o m i a l ?$
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