Mock AIME 2 2006-2007 Problems/Problem 8

Problem

The positive integers $\displaystyle x_1, x_2, ... , x_7$ satisfy $\displaystyle x_6 = 144$ and $\displaystyle x_{n+3} = x_{n+2}(x_{n+1}+x_n)$ for $\displaystyle n = 1, 2, 3, 4$ . Find the last three digits of $x_7$ .

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Mock AIME 2 2006-2007 Problems/Problem 8

Problem