  Solutions, exactly expressed in terms of elementary functions (unique
Laughlin states), of the correlated motion problem for a pair of 2D-electrons
in a constant and uniform magnetic field have been shown to exist for a certain
relation between the magnetic field induction and the electron charge.
Arguments that can help to understand the physical meaning of these remarkable
magnetic field values have been provided. The special interest to this problem
is justified by the importance of the new state of matter recently observed.
