Arya Bhatta Journal of Mathematics and Informatics

A set of three distinct polynomials with integer coefficients (a₁, a₂, a₃) is said to be Diophantine triple with D(n) if a_i = a_j + n is a perfect square for all 1 ≤ i, j ≤ 3, where n may be non-zero or polynomial with integer coefficients. A set of three distinct non-zero Gaussian integers is said to be a Gaussian Diophantine 3-tuple with property D (n) if the product of any two member of set with addition of n (a non-zero integer or a polynomial with integer coefficients or Gaussian integer) is a perfect square. This paper concerns with the study of construction of sequences of Diophantine triples (a,b,c) such that the product of any two elements of the set subtracted by a polynomial with integer coefficients is a perfect square with suitable properties.