@MISC{NUMERAL1.MIZ,
  AUTHOR = {Naumowicz, Adam},
  TITLE = {On the Representation of Natural Numbers in Positional Numeral Systems},
  NOTE = {This work has been partially supported by the FP6 IST grant TYPES No. 510996.},
  SECTION1 = {Preliminaries},
  SECTION2 = {Representation of Numbers in the Base-$b$ Numeral System},
  SECTION3 = {Selected Divisibility Criteria},
  DAY = {31},
  MONTH = {December},
  YEAR = {2006},
  ADDRESS1 = {Institute of Computer Science\\University of Bia{\l}ystok\\Akademicka 2, 15-267 Bia{\l}ystok, Poland},
  SUMMARY = {In this paper we show that every natural number
  can be uniquely represented as a base-$b$ numeral.
  The formalization is based on the proof presented
  in \cite{SIERPINSKI:1}. We also prove selected divisibility
  criteria in the base-$10$ numeral system.}}

