TR-MO-R1 2018 Problem 2

$x_0, x_1, \dots, x_{2018}$ tam sayıları $x_0 = 1$ , $x_1 = 2$ ve her $n \geq 1$ için $x_{n+1} = 3x_n - 2x_{n-1}$ koşulunu sağlıyorsa, $x_{2018}$ sayısının 2018 ile bölümünden kalan kaçtır?

a) 0 b) 2 c) 4 d) 6 e) 8

Official text Turkish Mathematical Olympiad, first round 2018 official paper, page 3. Quoted with source.

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