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A number v=xy with an even number n of digits formed by multiplying a pair of n/2-digit numbers (where the digits are taken from the original number in any order) x and y ...

Number theory is a vast and fascinating field of mathematics, sometimes called "higher arithmetic," consisting of the study of the properties of whole numbers. Primes and ...

A minimum clique covering is a clique covering of minimum size, and the size of such a minimum clique covering is known as the clique covering number. Note that while a ...

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

For any ideal I in a Dedekind ring, there is an ideal I_i such that II_i=z, (1) where z is a principal ideal, (i.e., an ideal of rank 1). Moreover, for a Dedekind ring with a ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

A number is said to be simply normal to base b if its base-b expansion has each digit appearing with average frequency tending to b^(-1). A normal number is an irrational ...

In common usage, an ordinal number is an adjective which describes the numerical position of an object, e.g., first, second, third, etc. In formal set theory, an ordinal ...

Consider the set of compact n-Riemannian manifolds M with diameter(M)<=d, Volume(M)>=V, and |K|<=kappa where kappa is the sectional curvature. Then there is a bound on the ...