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In computing and mathematics, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the...

each residue class modulo m. For example, the least residue system modulo 4 is {0, 1, 2, 3}. Some other complete residue systems modulo 4 include: {1, 2...

a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer...

In mathematics, the term modulo ("with respect to a modulus of", the Latin ablative of modulus which itself means "a small measure") is often used to assert...

non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n. Equivalently, the elements of this group can...

number theory, an integer q is a quadratic residue modulo n if it is congruent to a perfect square modulo n; that is, if there exists an integer x such that...

In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable...

(11 minus the remainder of the sum of the products modulo 11) modulo 11. Taking the remainder modulo 11 a second time accounts for the possibility that...

a3, ...) of real numbers is said to be equidistributed modulo 1 or uniformly distributed modulo 1 if the sequence of the fractional parts of an, denoted...

of an "accumulator" argument (product in the above example) to the function. Tail recursion modulo cons is a generalization of tail-recursion optimization...

described in the Examples section. In informal contexts, mathematicians often use the word modulo (or simply mod) for similar purposes, as in "modulo isomorphism"...

number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the...

remainder after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there is an infinite number of solutions of this congruence, which...

is that it will not break up clustered keys. For example, the keys 123000, 456000, 789000, etc. modulo 1000 all map to the same address. This technique...

1, or 2, where addition in the x-coordinate is modulo 2 and addition in the y-coordinate is modulo 3. These structures are isomorphic under addition...

{\displaystyle k} such that b k = a {\displaystyle b^{k}=a} . In arithmetic modulo an integer m {\displaystyle m} , the more commonly used term is index: One...

will be systematically in favor of small remainders.: Classic Modulo (Biased)  For example, assume that your random number source gives numbers from 0 to...

modulo a prime number p, then this root can be lifted to a unique root modulo any higher power of p. More generally, if a polynomial factors modulo p...

weighted sum of the digits, modulo 10, with different weights for each number position. To illustrate this, for example if the weights for a four digit...

by b and performing a modulo operation on the resulting product, thereby keeping the resulting c a small integer. The example b = 4, e = 13, and m =...