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If a is an arbitrary integer relatively prime to n and g is a primitive root of n, then there exists among the numbers 0, 1, 2, ..., phi(n)-1, where phi(n) is the totient ...

Dots and boxes is a two-person game based on a rectangular lattice of points. Each player, in turn, draws a horizontal or vertical line connecting two adjacent points. ...

A means of describing how one state develops into another state over the course of time. Technically, a dynamical system is a smooth action of the reals or the integers on ...

A (p,q)-graph is edge-graceful if the edges can be labeled 1 through q in such a way that the labels induced on the vertices by summing over incident edges modulo p are ...

A curve also known as the Gerono lemniscate. It is given by Cartesian coordinates x^4=a^2(x^2-y^2), (1) polar coordinates, r^2=a^2sec^4thetacos(2theta), (2) and parametric ...

An embedding is a representation of a topological object, manifold, graph, field, etc. in a certain space in such a way that its connectivity or algebraic properties are ...

If a complex function is analytic at all finite points of the complex plane C, then it is said to be entire, sometimes also called "integral" (Knopp 1996, p. 112). Any ...

Milnor (1956) found more than one smooth structure on the seven-dimensional hypersphere. Generalizations have subsequently been found in other dimensions. Using surgery ...

Consider an arbitrary one-dimensional map x_(n+1)=F(x_n) (1) (with implicit parameter r) at the onset of chaos. After a suitable rescaling, the Feigenbaum function ...

A subset E of a topological space S is said to be of first category in S if E can be written as the countable union of subsets which are nowhere dense in S, i.e., if E is ...