# Recurrence relation 2

Let $$x_{1},\ldots,x_{42}$$ be real numbers such that $$5x_{i+1} −x_{i} −3x_{i}x_{i+1} = 1$$ for each $$1 ≤ i ≤ 42$$, with $$x_{1} = x_{43}$$. Let the product of all possible values for $$x_{1} + x_{2} + \cdots + x_{42}=M$$, Number of possible values of $$x_{1} + x_{2} +\cdots + x_{42}=N$$ . Find $$N+M$$

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