  It is shown that there exist several ways to treat the quantum-mechanical
Coulomb problem for a Dirac particle in flat Minkowski space with the help of
the Heun differential equation, Fuchs's equation with four singular points.
When extending the problem to curved spaces of constant curvature, Lobachevsky
H_{3} and Rimann S_{3}, there arise 2-nd order differential equations of the
Fuchs type with 6 singular points, a method to get relevant equations with five
singular points has been elaborated.
