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Consecutive numbers (or more properly, consecutive integers) are integers n_1 and n_2 such that n_2-n_1=1, i.e., n_2 follows immediately after n_1. Given two consecutive ...

Legendre's formula counts the number of positive integers less than or equal to a number x which are not divisible by any of the first a primes, (1) where |_x_| is the floor ...

Let n be a positive integer and r(n) the number of (not necessarily distinct) prime factors of n (with r(1)=0). Let O(m) be the number of positive integers <=m with an odd ...

The reciprocal of a real or complex number z!=0 is its multiplicative inverse 1/z=z^(-1), i.e., z to the power -1. The reciprocal of zero is undefined. A plot of the ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

A palindromic prime is a number that is simultaneously palindromic and prime. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, ...

Given a number z, the cube root of z, denoted RadicalBox[z, 3] or z^(1/3) (z to the 1/3 power), is a number a such that a^3=z. The cube root is therefore an nth root with ...

A hyperbolic linear map R^n->R^n with integer entries in the transformation matrix and determinant +/-1 is an Anosov diffeomorphism of the n-torus, called an Anosov ...

Let X and Y be CW-complexes and let X_n (respectively Y_n) denote the n-skeleton of X (respectively Y). Then a continuous map f:X->Y is said to be cellular if it takes ...

A glome is a 4-sphere (in the geometer's sense of the word) x^2+y^2+z^2+w^2=r^2 (as opposed to the usual 3-sphere). The term derives from the Latin "glomus" meaning "ball of ...