Back to the index. Or to the chambers
This article has 20 links. View as Cloud or List.
Loading ...
Planetmath Browser (2008—2009)
BSD licence | A django site
All articles taken from PlanetMath.org snapshot under CC-BY-SA licence.
→ The original article on PlanetMath.org
Other Formats: LaTeX
Number Odd
An odd number 
is an integer
of the form 
, and as such it is not divisible
by 2. In terms
of congruences,
, and in its binary
representation
the least significant bit
is 1. With the exception of 2, all prime numbers
are odd numbers.
The addition
of two odd numbers gives an even number, or any even number of odd
summands gives an even number as a result. For example,
.
But the multiplication
of two odd numbers, or any even
amount of odd multiplicands always gives an odd number. For example,
.
A negative number
raised to the power of an odd number gives a negative number. For example,
(compare
).
The sum
of the first 
consecutive
positive
odd numbers is 
.
The famous Gregory series
which gives a quarter of 
is an alternating sum
of the reciprocals
of the odd numbers:
