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We study the quadratic integral pointsÐthat is, (S-)integral points defined over any extension of degree two of the base fieldÐon a curve defined in P 3 by a system of two Pell equations. Such points belong to three families explicitly described, or belong to a finite set whose cardinality may be explicitly bounded in terms of the base field, the equations defining the curve and the set S. We exploit the peculiar geometry of the curve to adapt the proof of a theorem of Vojta, which in this casedoi:10.4171/rsmup/126-3 fatcat:77dkqoattff2thv2ounanbbkli