Search results
Results from the WOW.Com Content Network
A modular multiplicative inverse of a modulo m can be found by using the extended Euclidean algorithm. The Euclidean algorithm determines the greatest common divisor (gcd) of two integers, say a and m. If a has a multiplicative inverse modulo m, this gcd must be 1. The last of several equations produced by the algorithm may be solved for this gcd.
A straightforward algorithm to multiply numbers in Montgomery form is therefore to multiply aR mod N, bR mod N, and R′ as integers and reduce modulo N. For example, to multiply 7 and 15 modulo 17 in Montgomery form, again with R = 100, compute the product of 3 and 4 to get 12 as above.
The multiplicative order of a number a modulo n is the order of a in the multiplicative group whose elements are the residues modulo n of the numbers coprime to n, and whose group operation is multiplication modulo n. This is the group of units of the ring Zn; it has φ (n) elements, φ being Euler's totient function, and is denoted as U (n) or ...
In 1933, Raymond Paley discovered the Paley construction, which produces a Hadamard matrix of order q + 1 when q is any prime power that is congruent to 3 modulo 4 and that produces a Hadamard matrix of order 2(q + 1) when q is a prime power that is congruent to 1 modulo 4. [5] His method uses finite fields.
Colombia 's architectural heritage includes Spanish colonial architecture, such as Catholic churches. Its modern architecture represents various International Style architecture. In the postmodern architecture era, a wave of innovate and striking buildings have been designed. Colombian cultural heritage includes indigenous, European, Indian and ...
State ( ICP) [1] The Museo de la Arquitectura Ponceña (Museum of Ponce Architecture) is an architecture museum housed at the Casa Wiechers-Villaronga, in Ponce, Puerto Rico. It is preserves the history of the architectural styles of Ponce and Puerto Rico. The Casa Wiechers-Villaronga was acquired and restored by the Institute of Puerto Rican ...
In a vector space, the additive inverse −v (often called the opposite vector of v) has the same magnitude as v and but the opposite direction. [9] In modular arithmetic, the modular additive inverse of x is the number a such that a + x ≡ 0 (mod n) and always exists. For example, the inverse of 3 modulo 11 is 8, as 3 + 8 ≡ 0 (mod 11). [10]
Inca architecture is the most significant pre-Columbian architecture in South America. The Incas inherited an architectural legacy from Tiwanaku, founded in the 2nd century B.C.E. in present-day Bolivia. A core characteristic of the architectural style was to use the topography and existing materials of the land as part of the design. [1]