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）
ON FINDING INTEGER SOLUTIONS TO SEXTIC EQUATION WITH FOUR UNKNOWNS xy(x+y)=8zw^5
Dr. J. Shanthi 1*, Dr. N. Thiruniraiselvi2 , Dr. M.A.Gopalan3
Abstract
This paper deals with the problem of finding non-zero distinct integer solutions to the non-homogeneous sextic equation with four unknowns given by xy(x+y) =8zw5.
Key words: Non-homogeneous Sextic , Sextic with four unknowns, integer solutions.
Mathematical Subject Classification 2010: 11D99.
Introduction
It is well-known that a diophantine equation is an algebraic equation with integer coefficients involving two or more unknowns such that the only solutions focused are integer solutions .No doubt that diophantine equations are rich in variety [1-4] .There is no universal method available to know whether a diophantine equation has a solution or finding all solutions if it exists .For equations with more than three variables and degree at least three, very little is known. It seems that much work has not been done in solving higher degree diophantine equations. While focusing the attention on solving sextic Diophantine equations with variables at least three ,the problems illustrated in [ 5-24 ] are observed. This paper focuses on finding integer solutions to the sextic equation with four unknowns xy(x+y) =8zw5.