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An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5 + 1 / 2 , 5/4, and √ 2 are not. [8] The integers form the smallest group and the smallest ring containing the natural 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.
In a complex plane, > is identified with the positive real axis, and is usually drawn as a horizontal ray. This ray is used as reference in the polar form of a complex number . The real positive axis corresponds to complex numbers z = | z | e i φ , {\displaystyle z=|z|\mathrm {e} ^{\mathrm {i} \varphi },} with argument φ = 0. {\displaystyle ...
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
A positive integer such that every smaller positive integer is a sum of distinct divisors of it is a practical number. By definition, a perfect number is a fixed point of the restricted divisor function s ( n ) = σ ( n ) − n , and the aliquot sequence associated with a perfect number is a constant sequence.
In number theory and combinatorics, a partition of a non-negative integer n, also called an integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. (If order matters, the sum becomes a composition.)
The greatest common divisor (GCD) of integers a and b, at least one of which is nonzero, is the greatest positive integer d such that d is a divisor of both a and b; that is, there are integers e and f such that a = de and b = df, and d is the largest such integer.
A square-free integer is an integer that is not divisible by any square other than 1. square number A square number is an integer that is the square of an integer. For example, 4 and 9 are squares, but 10 is not a square. Szpiro Szpiro's conjecture is, in a modified form, equivalent to the abc conjecture.