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starts over when the hour hand passes 12. We say that 15 is congruent to 3 modulo 12, written 15 ≡ 3 (mod 12), so that 7 + 8 ≡ 3 (mod 12). Similarly, if one...

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

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...

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...

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

π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats. Pisano periods are named after Leonardo Pisano, better known...

arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most...

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...

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...

general, may not be reduced modulo 2). It is then possible to reduce all coefficients modulo 2, which will give a modular form modulo 2. Modular forms are generated...

prime field of order p {\displaystyle p} may be constructed as the integers modulo p {\displaystyle p} , Z / p Z {\displaystyle \mathbb {Z} /p\mathbb {Z} }...

Modulo-N code is a lossy compression algorithm used to compress correlated data sources using modular arithmetic. When applied to two nodes in a network...

formulation used a shared-secret-key created from exponentiation of some number, modulo a prime number. However, they left open the problem of realizing a one-way...

algebraic terms, λ(n) is the exponent of the multiplicative group of integers modulo n. As this is a finite abelian group, there must exist an element whose...

0{\pmod {29}}\;\;{\text{ and }}\;\;5{F_{15}}^{2}=1860500\equiv 5{\pmod {29}}} For odd n, all odd prime divisors of Fn are congruent to 1 modulo 4, implying that...

(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...

{a}{p}}\right)={\begin{cases}1&{\text{if }}a{\text{ is a quadratic residue modulo }}p{\text{ and }}a\not \equiv 0{\pmod {p}},\\-1&{\text{if }}a{\text{ is a quadratic nonresidue...

+ r0 is any nonzero polynomial modulo 2 with at most t nonzero coefficients, then R(x) is not a multiple of P(x) modulo 2. If follows that the corresponding...

advantage and efficiency advantage for computing modulo to one period. Computing modulo 1 turn or modulo 2 half-turns can be losslessly and efficiently...