Search results
Results from the WOW.Com Content Network
For example, the expression "5 mod 2" evaluates to 1, because 5 divided by 2 has a quotient of 2 and a remainder of 1, while "9 mod 3" would evaluate to 0, because 9 divided by 3 has a quotient of 3 and a remainder of 0. Although typically performed with a and n both being integers, many computing systems now allow other types of numeric operands.
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 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 same remainder when divided by n.
0 2 ≡ 8 2 ≡ 16 2 ≡ 0 2 2 ≡ 6 2 ≡ 10 2 ≡ 14 2 ≡ 4 4 2 ≡ 12 2 ≡ 16. So a nonzero number is a residue mod 8, 16, etc., if and only if it is of the form 4 k (8n + 1). A number a relatively prime to an odd prime p is a residue modulo any power of p if and only if it is a residue modulo p. [8] If the modulus is p n, then p k a is a ...
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
n. In modular arithmetic, the integers coprime (relatively prime) to n from the set of n 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 be thought of as the congruence classes, also known as residues modulo n, that are coprime to n.
Dirichlet character. In analytic number theory and related branches of mathematics, a complex-valued arithmetic function is a Dirichlet character of modulus (where is a positive integer) if for all integers and : [1] that is, is completely multiplicative. ; that is, is periodic with period .
The Euclidean norm of a complex number is the absolute value (also called the modulus) of it, if the complex plane is identified with the Euclidean plane. This identification of the complex number x + i y {\displaystyle x+iy} as a vector in the Euclidean plane, makes the quantity x 2 + y 2 {\textstyle {\sqrt {x^{2}+y^{2}}}} (as first suggested ...