INTERNATIONAL RESEARCH JOURNAL OF MATHEMATICS, ENGINEERING & IT VOLUME-1, ISSUE-4 (August 2014) ISSN: (2349-0322) A Monthly Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories. International Research Journal of Mathematics, Engineering & IT (IRJMEIT) Website: www.aarf.asia . Email: editoraarf@gmail.com , editor@aarf.asia Page 16 CONSTRUCTION OF – DIO QUADRUPLES S.Vidhyalakshmi 1 , A.Kavitha 2 And M.A.Gopalan 3 1,2,3 Department of Mathematics, Shrimati Indira Gandhi College, Trichy-620002, India. ABSTRACT This paper concerns with the study of constructing special - Dio Quadruples such that the product of any two elements of the set increased by their sum and five is a perfect square. KEY WORDS DIOPHANTINE QUADRUPLES, PELL EQUATION. 2010 Mathematics subject classification 11D(99) INTRODUCTION The problem of constructing the sets with property that the product of any two of its distinct elements is one less than a square has a very long history and such sets were studied by Diophantus [5]. A set of m positive integers } ...... , { 2 1 m a a a is said to have the property D(n), if n a a j i  , a perfect square for all and such a set is called a Diophantine m-tuples with property D(n). Many mathematicians considered the construction of different formulations of Diophantine quadruples with the property D(n) for any arbitrary integer n and also for any linear polynomials in n. In this context, one may refer [1-4, 6- 14,17,21,22] for an extensive review of various problems on Diophantine quadruples. This paper aims at constructing special Dio – quadruple where the special mention is provided because it differs from the earlier one and the special Dio – quadruple is constructed where the product of any two members of the quadruple with the addition of the same members and the addition of five satisfies the required property. In this context, one may refer [15,16,18- 21]. METHOD OF ANALYSIS Let and be two integers such that is a perfect square.