# 2016 is absolutely awesome 14

Number Theory Level 5

Let $$f(a, b) =\dfrac{1}{a+b}$$ when $$a+b \ne 0$$.

Suppose that $$x, y, z$$ are distinct integers such that $$x+y +z = 2016$$ and $$f(f(x, y), z) = f(x, f(y, z))$$ (where both sides of the equation exist and are welldefined).

Compute $$y$$.

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