On the solutions of quartic Diophantine equations

Abstract

In this article, first, using the elliptic curve method, it is proved that the quartic Diophantine equations x^4-y^4=k(t^lambda-u^4{+-} v^4) for positive even lambda and integers k and t has infinitely many non-trivial rational solutions. Then, by direct ways, parametric solutions for equations x^4-y^4=k(t^3{+-} u^4-v^4) are found.