# Egyptian Fraction?

Let $$x, \space y,$$ and $$z$$ be positive real integer, with $$1000< x <y <z<2000$$ and satisfy the condition $$\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{7} + \dfrac{1}{x} + \dfrac{1}{y} + \dfrac{1}{z} + \dfrac{1}{45} = 1$$.

Given further that $$x$$ is divisible by 42, find $$x+y+z$$.

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