Definition:Odd Integer/Definition 3
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- $x \equiv 1 \pmod 2$
where the notation denotes congruence modulo $2$.
In the words of Euclid:
- An odd number is that which is not divisible into two equal parts, or that which differs by an unit from an even number.
- $1, 3, 5, 7, 9, 11, \ldots$