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In computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, called the modulus of the operation. Given two positive numbers a and n, a modulo n (often abbreviated as a mod n) is the remainder of the Euclidean division of a by n, where a is the dividend and n is the divisor. [1]
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor (x). Similarly, the ceiling function maps x to the least integer greater than or equal to x, denoted ⌈x⌉ or ceil (x).
Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that. and either R = 0 or the degree of R is lower than the degree of B. These conditions uniquely define Q and R ...
Modular exponentiation is the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus); that is, c = b e mod m. From the definition of division, it follows that 0 ≤ c < m. For example, given b = 5, e = 3 and m = 13, dividing 5 3 = 125 by 13 leaves a remainder of c = 8.
A greatest common divisor of p and q is a polynomial d that divides p and q, and such that every common divisor of p and q also divides d. Every pair of polynomials (not both zero) has a GCD if and only if F is a unique factorization domain. If F is a field and p and q are not both zero, a polynomial d is a greatest common divisor if and only ...
Keyboard shortcuts make it easier and quicker to perform some simple tasks in your AOL Mail. Access all shortcuts by pressing shift+? on your keyboard. All shortcuts are formatted for Windows computers, but most will work on a Mac by substituting Cmd for Ctrl or Option for Alt. General keyboard shortcuts
and −2 is the least absolute remainder. In the division of 42 by 5, we have: 42 = 8 × 5 + 2, and since 2 < 5/2, 2 is both the least positive remainder and the least absolute remainder. In these examples, the (negative) least absolute remainder is obtained from the least positive remainder by subtracting 5, which is d. This holds in general.
Bill Maher knows his suitors aren't exactly age-appropriate — and he doesn't care.. On the Oct. 20 episode of The Skinny Confidential's Him & Her podcast, the Real Time with Bill Maher host, 68 ...