On the length of D(±1)-tuples in imaginary quadratic rings

Let K be an imaginary quadratic field and O-K its ring of integers. Fix a rational integer e. A set {a(1), a(2), ... , a(m)} subset of O-K \ {0} is called a D(epsilon)-m-tuple in O-K if a(i)a(j)+ epsilon = x(ij)(2), where x(ij) is an element of O-K for all i, j such that 1 <= i < j <= m. Here, we prove the non-existence of D(epsilon)-m-tuples in O-K for epsilon is an element of {-1, 1} and m > 24.