In this paper we consider the inverse scattering problem for the following Hartree type equation: \[ i\frac{\partial u}{\partial t} = -\varDelta u + (|x|^{-\sigma} * |u|^2) u. \] We prove the uniqueness theorem on the inverse scattering problem with respect to the power $\sigma$.

In this note, we study the unit groups and class numbers of three classes of bicyclic biquadratic number fields. Following Wada and Zhang's methods, the unit group and class number of a bicyclic biquadratic number field can be represented by the fundamental units and class numbers of their quadratic subgroups. The reason why this method works in our case is that the fundamental unit of the quadratic subfields of our bicyclic biquadratic fields can be determined explicitly.

Using the theory of linear forms in logarithms and a result due to Adachi, we show that the title equation has only the trivial positive integral solution under some conditions.