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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Proving that there are no integral points on a union of hyperbolas

I have a curve C: (x^2±x-y^2+1)(x^2∓x-y^2) where x,y ∈ Z+ that I want to prove has no non-trivial integral points other than (0,0),(1,0),(0,±1). I am having a hard time coming up with a solution.
Raghav Bhutani's user avatar