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# Singly and doubly even

In mathematics an even integer, that is, a number that is divisible by 2, is called evenly even or doubly even if it is a multiple of 4, and oddly even or singly even if it is not. [1]

63 relations: Absolute value, Arf invariant, Aromaticity, Bott periodicity theorem, Coding theory, Cohomology, Combinatorics, Compact space, Continued fraction, Cyclic compound, Darts, Degenerate bilinear form, Difference of two squares, Differentiable manifold, Divisibility rule, Divisor, Electron configuration, Euclid, Even code, Feit–Thompson theorem, Fermat's theorem on sums of two squares, Geometric topology, Group theory, Half-integer, Hückel's rule, Integer, Integer factorization, Irrational number, Irreducible fraction, L-theory, List of finite simple groups, List of representations of e, Localization of a ring, Mathematics, Multiplicative group of integers modulo n, Multiplicity (mathematics), Nicomachus, Non-abelian group, Number theory, Order (group theory), Organic chemistry, Orientability, P-adic number, P-adic order, Parallelizable manifold, Parity (mathematics), Parity of zero, Pi bond, PlanetMath, Powerful number, ... Expand index (13 more) »

## Absolute value

In mathematics, the absolute value (or modulus) of a real number is the non-negative value of without regard to its sign.

## Arf invariant

In mathematics, the Arf invariant of a nonsingular quadratic form over a field of characteristic 2 was defined by Turkish mathematician when he started the systematic study of quadratic forms over arbitrary fields of characteristic 2.

## Aromaticity

In organic chemistry, the term aromaticity is formally used to describe an unusually stable nature of some flat rings of atoms.

## Bott periodicity theorem

In mathematics, the Bott periodicity theorem describes a periodicity in the homotopy groups of classical groups, discovered by, which proved to be of foundational significance for much further research, in particular in K-theory of stable complex vector bundles, as well as the stable homotopy groups of spheres.

## Coding theory

Coding theory is the study of the properties of codes and their fitness for a specific application.

## Cohomology

In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex.

## Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

## Compact space

In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other).

## Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

## Cyclic compound

A cyclic compound (ring compound) is a term for a compound in the field of chemistry in which one or more series of atoms in the compound is connected to form a ring.

## Darts

Darts is a form of throwing sport in which small missiles are thrown at a circular target (dartboard) fixed to a wall.

## Degenerate bilinear form

In mathematics, specifically linear algebra, a degenerate bilinear form on a vector space V is a bilinear form such that the map from V to V∗ (the dual space of V) given by is not an isomorphism.

## Difference of two squares

In mathematics, the difference of two squares is a squared (multiplied by itself) number subtracted from another squared number.

## Differentiable manifold

In mathematics, a differentiable manifold is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

## Divisibility rule

A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits.

## Divisor

In mathematics a divisor of an integer n, also called a factor of n, is an integer that can be multiplied by some other integer to produce n.

## Electron configuration

In atomic physics and quantum chemistry, the electron configuration is the distribution of electrons of an atom or molecule (or other physical structure) in atomic or molecular orbitals.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes called Euclid of Alexandria to distinguish him from Euclid of Megara, was a Greek mathematician, often referred to as the "Father of Geometry".

## Even code

A binary code is called an even code if the Hamming weight of each of its codewords is even.

## Feit–Thompson theorem

In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable.

## Fermat's theorem on sums of two squares

In additive number theory, Pierre de Fermat's theorem on sums of two squares states that an odd prime p is expressible as with x and y integers, if and only if For example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways: On the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares.

## Geometric topology

In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.

## Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

## Half-integer

In mathematics, a half-integer is a number of the form where n is an integer.

## Hückel's rule

In organic chemistry, Hückel's rule estimates whether a planar ring molecule will have aromatic properties.

## Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

## Integer factorization

In number theory, integer factorization is the decomposition of a composite number into a product of smaller integers.

## Irrational number

In mathematics, an irrational number is any real number that cannot be expressed as a ratio of integers.

## Irreducible fraction

An irreducible fraction (or fraction in lowest terms or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and -1, when negative numbers are considered).

## L-theory

In mathematics algebraic L-theory is the K-theory of quadratic forms; the term was coined by C. T. C. Wall, with L being used as the letter after K. Algebraic L-theory, also known as 'hermitian K-theory', is important in surgery theory.

## List of finite simple groups

In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups.

## List of representations of e

The mathematical constant ''e'' can be represented in a variety of ways as a real number.

## Localization of a ring

In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## Multiplicative group of integers modulo n

In modular arithmetic the set of congruence classes relatively prime to the modulus number, say n, form a group under multiplication called the multiplicative group of integers modulo n. It is also called the group of primitive residue classes modulo n. In the theory of rings, a branch of abstract algebra, it is described as the group of units of the ring of integers modulo n. (Units refers to elements with a multiplicative inverse.) This group is fundamental in number theory.

## Multiplicity (mathematics)

In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset.

## Nicomachus

Nicomachus or Nicomachus of Gerasa (Νικόμαχος; c. 60 &ndash; c. 120 CE) was an important mathematician in the ancient world and is best known for his works Introduction to Arithmetic and Manual of Harmonics in Greek.

## Non-abelian group

In mathematics, a nonabelian group, also sometimes called a noncommutative group, is a group (G, *) in which there are at least two elements a and b of G such that a * b ≠ b * a.

## Number theory

Number theory (or arithmeticEspecially in older sources; see two following notes.) is a branch of pure mathematics devoted primarily to the study of the integers.

## Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

## Organic chemistry

Organic chemistry is a chemistry subdiscipline involving the scientific study of the structure, properties, and reactions of organic compounds and organic materials, i.e., matter in its various forms that contain carbon atoms.

## Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

In mathematics the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number systems.

In number theory, for a given prime number, the -adic order or -adic additive valuation of a non-zero integer is the highest exponent ν such that ν divides.

## Parallelizable manifold

In mathematics, a differentiable manifold \scriptstyle M of dimension n is called parallelizable if there exist smooth vector fields on the manifold, such that at any point \scriptstyle p of \scriptstyle M the tangent vectors provide a basis of the tangent space at \scriptstyle p. Equivalently, the tangent bundle is a trivial bundle, so that the associated principal bundle of linear frames has a section on \scriptstyle M. A particular choice of such a basis of vector fields on \scriptstyle M is called a parallelization (or an absolute parallelism) of \scriptstyle M.

## Parity (mathematics)

Parity is a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd.

## Parity of zero

Zero is an even number.

## Pi bond

In chemistry, pi bonds (π bonds) are covalent chemical bonds where two lobes of one involved atomic orbital overlap two lobes of the other involved atomic orbital.

## PlanetMath

PlanetMath is a free, collaborative, online mathematics encyclopedia.

## Powerful number

A powerful number is a positive integer m such that for every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form m.

## Prime number

A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself.

## Pronic number

A pronic number, oblong number, rectangular number or heteromecic number, is a number which is the product of two consecutive integers, that is, n (n + 1).

## Proof by infinite descent

In mathematics, a proof by infinite descent is a particular kind of proof by contradiction which relies on the facts that the natural numbers are well ordered and that there are only a finite number of them that are smaller than any given one.

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

## Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero.

Reductio ad absurdum (Latin: "reduction to absurdity"; pl.: reductiones ad absurdum), also known as argumentum ad absurdum (Latin: argument to absurdity), is a common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial, or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance.

## Signature (topology)

In the mathematical field of topology, the signature is an integer invariant which is defined for an oriented manifold M of dimension d.

## Skew-symmetric graph

In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.

## Spin structure

In differential geometry, a spin structure on an orientable Riemannian manifold (M,g) allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry.

## Square root of 2

The square root of 2, written in mathematics as or 2^, is the positive algebraic number that, when multiplied by itself, gives the number 2.

## Surgery theory

In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.

## Topological K-theory

In mathematics, topological -theory is a branch of algebraic topology.

## Trigonometric functions

In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle.

## References

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