An odd number is an integerof the form ,
where is an integer.
The odd numbers are therefore ..., , ,
1, 3, 5, 7, ... (OEIS A005408), which are also
the gnomonic numbers. Integers which are not odd
are called even.

Odd numbers leave a remainder of 1 when divided by two, i.e., the congruence holds for odd . The oddness of a number is called its parity,
so an odd number has parity 1, while an even number has
parity 0.

Commission on Mathematics of the College Entrance Examination Board. Informal Deduction in Algebra: Properties of Odd and Even Numbers.
Princeton, NJ, 1959.Sloane, N. J. A. Sequence A005408/M2400
in "The On-Line Encyclopedia of Integer Sequences."Merzbach,
U. C. and Boyer, C. B. A
History of Mathematics, 3rd ed. New York: Wiley, p. 49, 1991.