Search results
Results from the WOW.Com Content Network
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
Modulo. 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 ...
Primitive root modulo. n. In modular arithmetic, a number g is 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 a coprime to n, there is some integer k for which gk ≡ a (mod n ). Such a value k is called the index or discrete logarithm ...
The quadratic excess E ( p) is the number of quadratic residues on the range (0, p /2) minus the number in the range ( p /2, p) (sequence A178153 in the OEIS ). For p congruent to 1 mod 4, the excess is zero, since −1 is a quadratic residue and the residues are symmetric under r ↔ p − r.
Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression " a ≡ b (mod n )", pronounced " a is congruent to b modulo n ", means that a − b is an integer multiple of n, or equivalently, a and b both share the ...
The Mk 14 Enhanced Battle Rifle (EBR) is an American military selective fire battle rifle, and a designated marksman rifle chambered for the 7.62×51mm NATO cartridge.It is a variant of the M14 battle rifle and was originally built for use with units of United States Special Operations Command, such as the United States Navy SEALs, Delta Force, and task specific Green Berets ODA teams/units.
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 ...
X ≡ 6 (mod 11) has common solutions since 5,7 and 11 are pairwise coprime. A solution is given by X = t 1 (7 × 11) × 4 + t 2 (5 × 11) × 4 + t 3 (5 × 7) × 6. where t 1 = 3 is the modular multiplicative inverse of 7 × 11 (mod 5), t 2 = 6 is the modular multiplicative inverse of 5 × 11 (mod 7) and t 3 = 6 is the modular multiplicative ...