The theory of the longitudinal magnetoresistance at high magnetic fields and low temperatures is reformulated to incorporate screened impurities or a random potential of rather arbitrary shape. Analytical expressions are derived for the density of states, the chemical potential, the quasi particle damping and the longitudinal conductivity. They include vertex corrections and are valid from the higher field Shubnikov-de Haas regime up to arbitrarily high fields. The theory contains no adjustible parameter except the potential correlation function. InSb is studied as an example and a comparison with the experiment yields field dependent screening parameters.