# Recursive Recursion - 1

Discrete Mathematics Level 5

$\large \begin{array} {l l } a_{n} & = a_{n+1}a_{n-1} - b_{n+1}b_{n-1} \\ b_{n} & = b_{n+1}a_{n-1} + a_{n+1}b_{n-1} \\ \end{array}$

Consider, two recursive relations defined as above with initial starting conditions $$a_{0} = 1$$, $$b_{0} = 2$$, $$a_{1} = 3$$ and $$b_{1} = 4$$.

If the value of $$a_{2015}^{2} + b_{2015}^{2}$$ can be expressed as $$\dfrac{x}{y}$$, where $$x$$, $$y$$ are coprime integers. Find the value of $$x+y$$.

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