On a manifold of the Laughlin problem unique solutions

The present paper has revealed that there exist exact solutions in the form of elementary functions (unique Laughlin's states) for certain relationships between the magnetic field induction and the value of the electron charge in the problem of correlated motion of two electrons in a constant and uniform magnetic field. The authors ha~e suggested a number of considerations that allow an understanding of the physical idea of these remarkable attributes of the magnetic field. The interest in this problem is associated with a new experimentally discovered state of the substance.