2016/07/28 by Sidokhine, Felix
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1607.08648
In our work we study the equations of the form aX4+bX2 Y2+cY4=dZ2 over Gaussian integers by a method of the resolvents. We study as a new equations X4+6X2 Y2+Y4=Z2 (Mordell's equation over ℤ[i]), X4+6(1+i)X2Y2+2iY4=Z2 and X4± Y4=(1+ i)Z2 and give the new proofs of the known theorems on X4+Y4=Z2 (Fermat - Hilbert), X4± Y4=iZ2 (Szabó - Najman).