Arithmetic of the integer quantum Hall effect

text of abstract (Integer quantum Hall effect (IQHE) has been analysed considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted and their variation is studied as a function of magnetic field. The number of current carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis attempts to answer certain basic questions besides providing a simple but complete understanding of IQHE.)