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A positive integer which is divisible by the sum of its digits, also called a Niven number (Kennedy et al. 1980) or a multidigital number (Kaprekar 1955). The first few are ...
Legendre's conjecture asserts that for every n there exists a prime p between n^2 and (n+1)^2 (Hardy and Wright 1979, p. 415; Ribenboim 1996, pp. 397-398). It is one of ...
The Lehmer cotangent expansion for which the convergence is slowest occurs when the inequality in the recurrence equation b_k>=b_(k-1)^2+b_(k-1)+1. (1) for ...
Given a square complex or real matrix A, a matrix norm ||A|| is a nonnegative number associated with A having the properties 1. ||A||>0 when A!=0 and ||A||=0 iff A=0, 2. ...
Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...
Define a = d(u,v)d(w,x) (1) b = d(u,w)d(v,x) (2) c = d(u,x)d(v,w), (3) where u, v, w, and x are vertices of a graph and d(i,j) is the graph distance between vertices i and j. ...
A quasiregular polyhedron is the solid region interior to two dual regular polyhedra with Schläfli symbols {p,q} and {q,p}. Quasiregular polyhedra are denoted using a ...
The field of semidefinite programming (SDP) or semidefinite optimization (SDO) deals with optimization problems over symmetric positive semidefinite matrix variables with ...
A two-dimensional map also called the Taylor-Greene-Chirikov map in some of the older literature and defined by I_(n+1) = I_n+Ksintheta_n (1) theta_(n+1) = theta_n+I_(n+1) ...
A sum-product number is a number n such that the sum of n's digits times the product of n's digit is n itself, for example 135=(1+3+5)(1·3·5). (1) Obviously, such a number ...
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