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Number theory
Industry: Mathematics
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Number theory
algorithm
Mathematics; Number theory
A group of rules and procedures for solving a problem in a series of steps. Algorithms are used in mathematics and in computer programs for figuring out solutions.
Galois fields
Mathematics; Number theory
A Galois field is a field with finite number of elements. Galois fields take one of two forms: Z p - The integers modulo some prime p . F p ^ n - The polynomials with coefficients ...
Carmichael number
Mathematics; Number theory
A Carmichael Number is a composite number which passes the Fermat pseudoprime test for all bases. There are an infinite number of Carmichael numbers - the smallest is 561=11*17*3.
common divisor
Mathematics; Number theory
A number that two or more other numbers can be divided by with a remainder of zero. The number 3 is a common divisor of both 9 and 15.
Gaussian integers
Mathematics; Number theory
The ring of Gaussian integers is the extension of the integers with a symbol i which is the root of the equation x 2 =-1. Thus this ring consists of elements of the form ( n + m * i ) with the ...
abelian group
Mathematics; Number theory
An abelian group is a group whose operation is commutative, ie a * b = b * a . An example of an abelian group is the integers with the usual addition operation. An example of a group which is not ...
composite
Mathematics; Number theory
A composite number has non-trivial factors, ie factors other than itself and 1. Thus 13 is prime but 15=3*5 is composite. A number which is not composite is called prime. A polynomial which has ...
