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A school identification number in Bali, written with Balinese numerals above and Arabic numerals below. The numerals 1–10 have basic, combining, and independent forms, many of which are formed through reduplication. The combining forms are used to form higher numbers.
Prime number: A positive integer with exactly two positive divisors: itself and 1. The primes form an infinite sequence 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ... Composite number: A positive integer that can be factored into a product of smaller positive integers. Every integer greater than one is either prime or composite.
The integers consist of 0, the natural numbers (1, 2, 3, ...), and their negatives (−1, −2, −3, ...). The set of all integers is usually denoted by Z (or Z in blackboard bold, ), which stands for Zahlen (German for "numbers"). Articles about integers are automatically sorted in numerical order.
The smallest integer m > 1 such that p n # + m is a prime number, where the primorial p n # is the product of the first n prime numbers. A005235: Semiperfect numbers:
The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the French word entier, which means both entire and integer. [9] Historically the term was used for a number that was a multiple of 1, [10] [11] or to the whole part of a ...
Sigma function: Sums of powers of divisors of a given natural number. Euler's totient function: Number of numbers coprime to (and not bigger than) a given one. Prime-counting function: Number of primes less than or equal to a given number. Partition function: Order-independent count of ways to write a given positive integer as a sum of positive ...
The history of discrete mathematics has involved a number of challenging problems which have focused attention within areas of the field. In graph theory, much research was motivated by attempts to prove the four color theorem , first stated in 1852, but not proved until 1976 (by Kenneth Appel and Wolfgang Haken, using substantial computer ...
An even number is an integer that is "evenly divisible" by two, that is divisible by two without remainder; an odd number is an integer that is not even. (The old-fashioned term "evenly divisible" is now almost always shortened to "divisible".) Any odd number n may be constructed by the formula n = 2k + 1, for a suitable integer k.