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A univariate function f(x) is said to be odd provided that f(-x)=-f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, ...

An odd chordless cycle is a chordless cycle of length >4. A graph is said to be perfect iff neither the graph G nor its graph complement G^_ has an odd chordless cycle. A ...

A Berge graph is a simple graph that contains no odd graph hole and no odd graph antihole. The strong perfect graph theorem asserts that a graph is perfect iff it is a Berge ...

The sum of the first n odd numbers is a square number, sum_(k=1)^n(2k-1)=n^2. A sort of converse also exists, namely the difference of the nth and (n-1)st square numbers is ...

If a sequence of double points is passed as a closed curve is traversed, each double point appears once in an even place and once in an odd place.

An odd permutation is a permutation obtainable from an odd number of two-element swaps, i.e., a permutation with permutation symbol equal to -1. For initial set {1,2,3,4}, ...

An odd power is a number of the form m^n for m>0 an integer and n a positive odd integer. The first few odd powers are 1, 8, 27, 32, 64, 125, 128, 216, 243, 343, 512, ... ...

For N=k·2^n+1 with k odd and 2^n>k, if there exists an integer a such that a^((N-1)/2)=-1 (mod N), then N is prime. A prime of this form is known as a Proth prime.

A method for constructing magic squares of odd order, also called de la Loubere's method.

The twin composites may be defined by analogy with the twin primes as pairs of composite numbers (n,n+2). Since all even number are trivially twin composites, it is natural ...