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A 10-digit number satisfying the following property. Number the digits 0 to 9, and let digit n be the number of ns in the number. There is exactly one such number: 6210001000.

Let the residue from Pépin's theorem be R_n=3^((F_n-1)/2) (mod F_n), where F_n is a Fermat number. Selfridge and Hurwitz use R_n (mod 2^(35)-1,2^(36),2^(36)-1). A ...

Given an ideal A, a semiprime ring is one for which A^n=0 implies A=0 for any positive n. Every prime ring is semiprime.

A semiprime ring which is also an Artinian ring.

When a prime l divides the elliptic discriminant of a elliptic curve E, two or all three roots of E become congruent (mod l). An elliptic curve is semistable if, for all such ...

A graph G is said to be separable if it is either disconnected or can be disconnected by removing one vertex, called articulation. A graph that is not separable is said to be ...

Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...

An array B=b_(ij), i,j>=1 of positive integers is called a dispersion if 1. The first column of B is a strictly increasing sequence, and there exists a strictly increasing ...

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

A set partition of a set S is a collection of disjoint subsets of S whose union is S. The number of partitions of the set {k}_(k=1)^n is called a Bell number.