On the resolution of index form equations in biquadratic number fields, I

AbstractIn this paper we develop a method for computing all small solutions (i.e. with coordinates of absolute value <107) of index form equations in totally real biquadratic number fields. If the index form equation is not solvable, this will also be recognized by our algorithm in most cases. As an application we present all such solutions in quadratic extensions K of Q(√5) of discriminant DKQ < 63000 and of Q(√2) of discriminant DKQ < 39000