@misc{NEWTON04.MIZ,
  AUTHOR = {Ziobro, Rafa{\l}},
  TITLE = {On Subnomials},
  ADDRESS1 = {Department of Carbohydrate Technology, University of Agriculture in Krakow},
  DAY = {18},
  MONTH = {October},
  YEAR = {2016},
  ACKNOWLEDGEMENT = {Ad Maiorem Dei Gloriam},
  SUMMARY = {While discussing the sum of consecutive powers as a result of division of two binomials W.W. Sawyer observes
    ``It is a curious fact that most algebra textbooks give our ast result twice.
  It appears in two different chapters and usually there is no mention in
    either of these that it also occurs in the other. The first chapter, of course,
   is that on factors. The second is that on geometrical progressions.
  Geometrical progressions are involved in nearly all financial questions involving
  compound interest -- mortgages, annuities, etc." \cite{sawyer1970}.
  It's worth noticing that the first issue involves a simple arithmetical division of 99...9 by 9.
  While the above notion seems not to be changed over the last 50 years, it reflect only a special case
  of a broader class of problems involving two variables.
  It seems strange, that while binomial formula is discussed and studied widely, little research is
  done on its counterpart with all coefficients equal to one, which we will call here the subnomial.
  The study focuses on its basic properties and applies it
  to some simple problems usually proven by induction
 \cite{gancarzewicz2000}.}}

@misc{sawyer1970,
title={The Search for Pattern},
author={W.W. Sawyer},
year={1970},
publisher={Penguin Books Ltd, Harmondsworth, Middlessex, England}
}


@misc{gancarzewicz2000,
title={Arytmetyka},
author={Gancarzewicz, Jacek},
year={2000},
publisher={Wydawnictwo UJ, Krak{\'o}w}
}
