@misc{NEWTON05.MIZ,
AUTHOR = {Ziobro, Rafa{\l}},
TITLE = {Parity as a Property of Integers},
ADDRESS1 = {Department of Carbohydrate Technology, University of Agriculture in Krakow},
DAY = {29},
MONTH = {June},
YEAR = {2018},
KEYWORDS = {even, odd, divisibility, binary representation},
MSC2010 = {11A51, 03B35},
ACKNOWLEDGEMENT = {Ad Maiorem Dei Gloriam},
SUMMARY = {Even and odd numbers appear early in history of mathematics
 \cite{Zazkis1998}, as they
 serve to describe the property of objects
 easily noticeable by human eye \cite{sawyer2003vision}.
 Although the use of
 parity allowed to discover irrational numbers \cite{russo2013forgotten},
 there is
 a common opinion that this property is "not rich enough to become the main
 content focus of any
 particular research" \cite{Zazkis1998}.
 On the other hand, due to the use of decimal system, divisibility by 2
 is often regarded as the property of the last digit of a number
 (similarly to divisibility by 5, but not to divisibility by
 any other primes), which probably restricts its use for any advanced
 purposes.
 The article aims to extend the definition of parity
 towards its notion in binary representation of integers, thus
  making an alternative to the articles grouped in
  \cite{BINARITH.ABS}, \cite{NUMERAL1.ABS},
  and \cite{RADIX_1.ABS} branches.}}

@book{russo2013forgotten,
title={The forgotten revolution: how science was born
in 300 BC and why it had to be reborn},
author={Russo, Lucio and others},
year={2013},
publisher={Springer Science \& Business Media}
}

@book{sawyer2003vision,
  title={Vision in elementary mathematics},
  author={Sawyer, Walter Warwick},
  year={2003},
  publisher={Courier Corporation}
}

@Article{Zazkis1998,
author="Zazkis, Rina",
title="Odds and Ends of Odds and Evens: An Inquiry Into Students' Understanding of Even and Odd Numbers",
journal="Educational Studies in Mathematics",
year="1998",
month="Jun",
day="01",
volume="36",
number="1",
pages="73--89",
issn="1573-0816",
doi="10.1023/A:1003149901409",
url="https://doi.org/10.1023/A:1003149901409"
}

