\(x^{p} + y^{q} = y^{r} + z^{p} = z^{q} + x^{r}\), x, y and z are positive reals, p, q, and r are positive integers. Find all values of x,y,z,p,q,r. General solutions are acceptable (i.e. x=y=z, p=q=r). How would I go about solving this?

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