Summary: We prove that for any integer \(m\) (different from \(0, +2, -2\)), there are infinitely many positive integers \(D\) for which the form \(x^2 - Dy^2\) primitively represents \(m, -m\), and \(-1\). We do this by constructing an infinite sequence of such \(D\)’s associated with each \(m\). Also, when \(m\) is odd, we relate the existence of additional such \(D\)’s to well-known conjectures.