# Obligatory Six Afraid of Seven Joke

Number Theory Level 4

The positive integers $$x_{1}\ldots,x_{7}$$ satisfy the condition $$x_{6}=144$$ and $x_{n+3}=x_{n+2}(x_{n+1}+x_{n})$ where $$n = 1,2,3,4$$ Then what is the value of $$x_{7}$$

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