Diophantine tuples and Integral Ideals of Q(√d)

Suppose n is the fundamental discriminant associated with a quadratic extension of Q. We show that for every Diophantine m-tuple ₁, t₂, …, tₘ\ with the property $ D(n) $, there exists integral ideals t₁, t₂, …, tₘ of Q(√n) and c∈ \1,2\ such that tᵢ= cN(tᵢ) for i=1,2, …, m. Here, N(·) denotes the norm map from Q(√n) to Q. Moreover, we explicitly construct the above ideals for Diophantine pairs ₁, a₂\ whenever (a₁, a₂) = 1.