The rational integral solution of the equation a(x³+y³)=b(u³+v³) and allied Diophantine equations

We prove that for each n ∈ ℕ₊ the Diophantine equation A² ± nB⁴ + C⁴ = D⁸ has infinitely many primitive integer solutions, i.e. solutions satisfying gcd(A,B,C,D) = 1.

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