In this paper, we prove that there does not exist a set of four positive integers {3, 6, c, d}, such that a product of any two of them increased by 3 is a triangular number.

In this paper, we show that there is no polynomialD(n)-quadruple in ℤ[X] for some polynomialsn∈ ℤ[X] that are not representable as a difference of squares of two polynomials in ℤ[X].