Number theory

Number theory

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Number theory

strong pseudoprime test

Mathematics; Number theory

A pseudoprime test. Let N -1 = 2 s q . If there is some r in the range 0 r s such that b ( N -1)/2^ r =-1(mod N ) and b ( N -1)/2^( r -1) =1(mod N ) then N is called an strong ...

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 ...

extension

Mathematics; Number theory

A field E is called an extension of another field F if F is contained in E as a subfield. Examples include the Galois fields, as they are all extensions of the integers modulo a prime p .

factor

Mathematics; Number theory

Factors are used to separate a number (or a polynomial) into a product of other numbers. These other numbers are called factors. Thus 15 is factored as 15=3*5. A non-trivial factorization has no ...

field

Mathematics; Number theory

A field is an algebraic structure with two operators (commonly called addition (+) and multiplication (*)) which satisfies the condition that elements of the field form an Abelian group under ...

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.