What are all the positive integers that satisfy this equation?

[donglepuss]

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

what are all the positive integers for x,y, z that satisfy this equation?

 

[jedishrfu]

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.