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Somer–Lucas Pseudoprime
In mathematics, specifically number theory, an odd number, odd and composite number ''N'' is a Somer–Lucas ''d''-pseudoprime (with given ''d'' ≥ 1) if there exists a nondegenerate Lucas sequence U(P,Q) with the discriminant D=P^2-4Q, such that \gcd(N,D)=1 and the rank appearance of ''N'' in the sequence ''U''(''P'', ''Q'') is :\frac\left(N-\left(\frac\right)\right), where \left(\frac\right) is the Jacobi symbol. Applications Unlike the standard Lucas pseudoprimes, there is no known efficient primality test using the Lucas ''d''-pseudoprimes. Hence they are not generally used for computation. See also Lawrence Somer, in his 1985 thesis, also defined the Somer d-pseudoprimes. They are described in brief on page 117 of Ribenbaum 1996. References * * * * {{DEFAULTSORT:Somer-Lucas Pseudoprime Pseudoprimes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
