De, Prithwijit
(2018)
The oddeven
tale.
At Right Angles, 7 (2).
pp. 126129.
ISSN 25821873
Abstract
We are introduced to the concept of an even
number and an odd number in primary school or
even earlier. Any natural number divisible by 2 is
even; if it is not, it is odd. The definition is extended to
integers once we learn the arithmetic of negative whole
numbers. Then we make simple observations such as: the
sum of two even numbers is even, as is the sum of two odd
numbers, and sum of an even number and an odd number is
odd. Carrying on, we deduce that the sum of an even
number of even numbers or odd numbers is even, and so is
the sum of an odd number of even numbers, whereas the
sum of an odd number of odd numbers is odd. This article
aims at discussing some problems where these simple
observations come into play.
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