# To bound or not to bound!

Consider the following diophantine equation in natural numbers$x+y^2+z^3=xyz$where $$z=\gcd(x,y)$$. Let $$(x_1,y_1,z_1), (x_2,y_2,z_2), ..., (x_n,y_n,z_n)$$ be the all triples which satisfy the equation. Find$\sum_{k=1}^{n} (x_k+y_k+z_k).$

Details and Assumptions

$$\gcd(a,b)$$ is the greatest common divisor of $$a$$ and $$b$$.

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