This book has three sections I, II and III. Section I deals with the study of formulation of special family of 3-tuples such that the product of any two elements of the set subtracted with their sum is a perfect square. Section II concerns with the process of obtaining family of 3-tuples such that the product of any two elements of the set added with their sum is a perfect square. Section III illustrates the construction of family of 3- tuples such that the sum of any two members of the set is a perfect square.