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A divisor, also called a factor, of a number n is a number d which divides n (written d|n). For integers, only positive divisors are usually considered, though obviously the ...

1729 is sometimes called the Hardy-Ramanujan number. It is the smallest taxicab number, i.e., the smallest number which can be expressed as the sum of two cubes in two ...

The ABC (atom-bond connectivity) spectral radius rho_(ABC) of a graph is defined as the largest eigenvalue of its ABC matrix. Chen (2019) showed that for a tree on 3 or more ...

An abstract manifold is a manifold in the context of an abstract space with no particular embedding, or representation in mind. It is a topological space with an atlas of ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

Algebraic geometry is the study of geometries that come from algebra, in particular, from rings. In classical algebraic geometry, the algebra is the ring of polynomials, and ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

Given a point P and a line AB, draw the perpendicular through P and call it PC. Let PD be any other line from P which meets CB in D. In a hyperbolic geometry, as D moves off ...

Many authors (e.g., Mendelson 1963; Pervin 1964) use the term arcwise-connected as a synonym for pathwise-connected. Other authors (e.g., Armstrong 1983; Cullen 1968; and ...