On $A^{2} \pm nB^{4} + C^{4} = D^{8}$
Volume 136 / 2014
Colloquium Mathematicum 136 (2014), 255-257
MSC: Primary 11D41; Secondary 11D72.
DOI: 10.4064/cm136-2-6
Abstract
We prove that for each $n\in \mathbb {N_{+}}$ the Diophantine equation $ A^2 \pm nB^4 + C^4 = D^8$ has infinitely many primitive integer solutions, i.e. solutions satisfying ${\rm gcd}(A, B, C, D) =1$.
