In mathematics, the transposable integers are integers that permute or shift cyclically when they are multiplied by another integer n {\displaystyle n}...

another pitch. The transposition of a set A by n semitones is designated by Tn(A), representing the addition (mod 12) of an integer n to each of the pitch...

numbers as the non-negative integers 0, 1, 2, 3, ..., while others start with 1, defining them as the positive integers 1, 2, 3, ... . Some authors acknowledge...

integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers...

non-singleton cycles in the in-situ transposition of a rectangular j X k matrix)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane...

positive integer N is a non-square number, its square root is irrational, we can equivalently prove its contrapositive, that if a positive integer N has...

In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For...

(product) of transpositions—formally, they are generators for the group. In fact, when the set being permuted is {1, 2, ..., n} for some integer n, then any...

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known...

A128858 in the OEIS) Cyclic number Linear-feedback shift register Transposable integer Dawidoff, Nicholas (March 25, 2009), "The Civil Heretic", New York...

number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one...

trial division, tests whether ⁠ n {\displaystyle n} ⁠ is a multiple of any integer between 2 and ⁠ n {\displaystyle {\sqrt {n}}} ⁠. Faster algorithms include...

positive integer, n! is the product of the first n positive integers, and is read as "n factorial". 2.  Double factorial: if n is a positive integer, n!!...

length(a)], b[1..length(b)] output: distance, integer let d[0..length(a), 0..length(b)] be a 2-d array of integers, dimensions length(a)+1, length(b)+1 // note...

number of the form 2n where n is an integer, that is, the result of exponentiation with number two as the base and integer n as the exponent. In the fast-growing...

32-bit integer. Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use the value directly, whereas the 64-bit integer Long...

numbers: the base, b, and the exponent or power, n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that...

form 4t + 3, for some integer t. Integers of this form are referred to as Blum primes. This means that the factors of a Blum integer are Gaussian primes...

of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition...

square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix...

number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is...

unsigned integers can accommodate all valid IBAN values. 231 is approximately equal to 2.1 × 109, making it possible for any 9-digit integer to be handled...

Hermitian if k {\displaystyle k} is an even integer and skew-Hermitian if k {\displaystyle k} is an odd integer. A {\displaystyle A} is skew-Hermitian if...

of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer n. They are named after Marin Mersenne, a French Minim friar, who studied...

is in {0,1}, that is, xi is a binary integer variable. Therefore, such constraints can be used to model any integer program with binary variables, which...

a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive...

number of the form 3n where n is an integer, that is, the result of exponentiation with number three as the base and integer n as the exponent. The powers of...

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number...

excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number...

∎ By definition, if n is an odd integer, it can be expressed as n = 2 k + 1 {\displaystyle n=2k+1} for some integer k. Thus n 2 = ( 2 k + 1 ) 2 = ( 2...