Quadratic Integral Solutions to Double Pell Equations
Francesco VenezianoScuola Normale Superiore, Pisa, Italy
We study the quadratic integral points--that is, (-)integral points defined over any extension of degree two of the base field--on a curve defined in 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 . We exploit the peculiar geometry of the curve to adapt the proof of a theorem of Vojta, which in this case does not apply.
Cite this article
Francesco Veneziano, Quadratic Integral Solutions to Double Pell Equations. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 47–61DOI 10.4171/RSMUP/126-3