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An infinite sequence {a_i} of positive integers is called weakly independent if any relation sumepsilon_ia_i with epsilon_i=0 or +/-1 and epsilon_i=0, except finitely often, ...

A weighted graph is a graph in which each branch is given a numerical weight. A weighted graph is therefore a special type of labeled graph in which the labels are numbers ...

Every nonempty set of positive integers contains a smallest member.

The constant polynomial P(x)=0 whose coefficients are all equal to 0. The corresponding polynomial function is the constant function with value 0, also called the zero map. ...

A number that is "close" to (but not equal to) zero may be called an almost zero. In contrast, a number or expression that is equal to zero is said to be identically zero. ...

If, for n and d integers, the ratio n/d is itself an integer, then d is said to divide n. This relationship is written d|n, read "d divides n." In this case, n is also said ...

Let S_N(s)=sum_(n=1)^infty[(n^(1/N))]^(-s), (1) where [x] denotes nearest integer function, i.e., the integer closest to x. For s>3, S_2(s) = 2zeta(s-1) (2) S_3(s) = ...

An irreducible algebraic integer which has the property that, if it divides the product of two algebraic integers, then it divides at least one of the factors. 1 and -1 are ...

An integer matrix whose entries satisfy a_(ij)={0 if j>i+1; -1 if j=i+1; 0 or 1 if j<=i. (1) There are 2^(n-1) special minimal matrices of size n×n.

The "Cartesian ovals," sometimes also known as the Cartesian curve or oval of Descartes, are the quartic curve consisting of two ovals. They were first studied by Descartes ...