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Divisibilityhard
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Let a sequence be defined by x0=2x_0 = 2x0​=2, x1=3x_1 = 3x1​=3, and xn+1=3xn−2xn−1x_{n+1} = 3x_n - 2x_{n-1}xn+1​=3xn​−2xn−1​ for n≥1n \ge 1n≥1. For which of the following relations between mmm and nnn is xnx_nxn​ guaranteed to divide xmx_mxm​?