JOURNAL OF LIAONING TECHNICAL UNIVERSITY
(NATURAL SCIENCE EDITION)
LIAONING GONGCHENG JISHU DAXUE XUEBAO (ZIRAN KEXUE BAN)
辽宁工程技术大学学报（自然科学版）
DELINEATION OF INTEGER SOLUTIONS TO HOMOGENEOUS BI-QUADRATIC EQUATION WITH FOUR UNKNOWNS x^4+y^4+z^4=18w^4
Dr. N. Thiruniraiselvi1*, Dr. M.A.Gopalan2
Abstract
The main thrust of this paper is to search for various choices of integer solutions to the homogeneous bi-quadratic equation with four unknowns given by x4+y4+z4 =18w4
Keywords: Homogeneous bi-quadratic, Bi-quadratic with four unknowns, Integer solutions
INTRODUCTION
The theory of Diophantine equations offers a rich variety of fascinating problems. In particular, biquadratic Diophantine equations, homogeneous and non-homogeneous have aroused the interest of numerous mathematicians since antiquity [1-5]. In this context, one may refer [6-24] for various problems on the biquadratic Diophantine equations with four variables. However, often we come across homogeneous biquadratic equations and as such one may require its integral solution in its most general form. It is towards this end, this paper concerns with the problem of determining non-trivial integral solutions of the homogeneous equation with four unknowns given by x4+y4+z4 =18w4 is analyzed for obtaining different sets of non-zero distinct integer solutions through employing the linear transformations.