Search Results for ""

A graph is planar if it can be drawn in a plane without graph edges crossing (i.e., it has graph crossing number 0). The number of planar graphs with n=1, 2, ... nodes are 1, ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...

A positive integer n is kth powerfree if there is no number d such that d^k|n (d^k divides n), i.e., there are no kth powers or higher in the prime factorization of n. A ...

A factorial prime is a prime number of the form n!+/-1, where n! is a factorial. n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

If alpha is any number and m and n are integers, then there is a rational number m/n for which |alpha-m/n|<=1/n. (1) If alpha is irrational and k is any whole number, there ...

A number D that possesses no common divisor with a prime number p is either a quadratic residue or nonresidue of p, depending whether D^((p-1)/2) is congruent mod p to +/-1.

A set partition of a set S is a collection of disjoint subsets of S whose union is S. The number of partitions of the set {k}_(k=1)^n is called a Bell number.

The logarithm of the reciprocal of a number, equal to the negative of the logarithm of the number itself, cologx=log(1/x)=-logx.

The fifth of Peano's axioms, which states: If a set S of numbers contains zero and also the successor of every number in S, then every number is in S.