What are all the positive integers that satisfy this equation?

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SUMMARY

The equation X3 + Y2 - Z = Z3 - X2 + Y has positive integer solutions. Specifically, the integer 1 satisfies the equation for all variables X, Y, and Z. This indicates that the equation holds true universally for the smallest positive integer, establishing a foundational solution. Further exploration may reveal additional solutions or constraints based on the values of X, Y, and Z.

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X^3 + y^2 - z = z^3 - x^2 + y

what are all the positive integers for x,y, z that satisfy this equation?
 
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What is the context for this problem? Is this a homework question?

if x,y,z can be any positive integer then 1 works for all.
 

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