Solution of certain Diophantine equations in Gaussian integers

Arkabarata Ghosh

In this article, we show that the quartic Diophantine equations $x^4\pm pq{y}^4=\pm z^2$ and $x^4\pm pq{y}^4=\pm i{z}^2$ have only trivial solutions for some primes $p$ and $q$ sati…