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The properties involving multiplication, division, and exponentiation generally require that a and n are integers. Identity: (a mod n) mod n = a mod n. nx mod n = 0 for all positive integer values of x. If p is a prime number which is not a divisor of b, then abp−1 mod p = a mod p, due to Fermat's little theorem.
If k a ≡ k b (mod m) and k is coprime with m, then a ≡ b (mod m). If k a ≡ k b (mod k m) and k ≠ 0, then a ≡ b (mod m). The last rule can be used to move modular arithmetic into division. If b divides a, then (a/b) mod m = (a mod b m) / b. The modular multiplicative inverse is defined by the following rules:
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.
The cell cycle in eukaryotes: I = Interphase, M = Mitosis, G 0 = Gap 0, G 1 = Gap 1, G 2 = Gap 2, S = Synthesis, G 3 = Gap 3. Cell division is the process by which a parent cell divides into two daughter cells. [1] Cell division usually occurs as part of a larger cell cycle in which the cell grows and replicates its chromosome (s) before dividing.
Montgomery modular multiplication relies on a special representation of numbers called Montgomery form. The algorithm uses the Montgomery forms of a and b to efficiently compute the Montgomery form of ab mod N. The efficiency comes from avoiding expensive division operations. Classical modular multiplication reduces the double-width product ab ...
Operator (mathematics) In mathematics, an operator is generally a mapping or function that acts on elements of a space to produce elements of another space (possibly and sometimes required to be the same space). There is no general definition of an operator, but the term is often used in place of function when the domain is a set of functions ...
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p. -adic analysis. In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p -adic numbers. The theory of complex-valued numerical functions on the p -adic numbers is part of the theory of locally compact groups. The usual meaning taken for p -adic analysis is the theory of p -adic ...