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The nth taxicab number Ta(n) is the smallest number representable in n ways as a sum of positive cubes. The numbers derive their name from the Hardy-Ramanujan number Ta(2) = ...

The Schur number S(k) is the largest integer n for which the interval [1,n] can be partitioned into k sum-free sets (Fredricksen and Sweet 2000). S(k) is guaranteed to exist ...

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

The Skewes number (or first Skewes number) is the number Sk_1 above which pi(n)<li(n) must fail (assuming that the Riemann hypothesis is true), where pi(n) is the prime ...

A harmonic number is a number of the form H_n=sum_(k=1)^n1/k (1) arising from truncation of the harmonic series. A harmonic number can be expressed analytically as ...

In algebra, a period is a number that can be written an integral of an algebraic function over an algebraic domain. More specifically, a period is a real number ...

The real axis is the line in the complex plane corresponding to zero imaginary part, I[z]=0. Every real number corresponds to a unique point on the real axis.

Every real number is negative, 0, or positive. The law is sometimes stated as "For arbitrary real numbers a and b, exactly one of the relations a<b, a=b, a>b holds" (Apostol ...

In Book IX of The Elements, Euclid gave a method for constructing perfect numbers (Dickson 2005, p. 3), although this method applies only to even perfect numbers. In a 1638 ...