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Consider the sum (1) where the x_js are nonnegative and the denominators are positive. Shapiro (1954) asked if f_n(x_1,x_2,...,x_n)>=1/2n (2) for all n. It turns out ...

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

The cross number of a zero-system sigma={g_1,g_2,...,g_n} of G is defined as K(sigma)=sum_(i=1)^n1/(|g_i|) The cross number of a group G has two different definitions. 1. ...

If r is an algebraic number of degree n, then the totality of all expressions that can be constructed from r by repeated additions, subtractions, multiplications, and ...

Number Theory

R. C. Read defined the anarboricity of a graph G as the maximum number of edge-disjoint nonacyclic (i.e., cyclic) subgraphs of G whose union is G (Harary and Palmer 1973, p. ...

An odd alternating permutation number, more commonly called an Euler number or secant number.

An even alternating permutation number, more commonly called a tangent number.

Betti numbers are topological objects which were proved to be invariants by Poincaré, and used by him to extend the polyhedral formula to higher dimensional spaces. ...

The algebraic integers in a number field.