Multiply monogenic orders

An order of a number field is called monogenic if it is generated by a single element over the integers. Clearly, if an order is generated by an algebraic number, then it is generated by any translate of this number by a rational integer. Such numbers are called equivalent. In the present talk we will be interested in orders having two or more pairwise non-equivalent generators. Joint work with J.-H. Evertse and K. Győry.