Relativistic Breit–Wigner distribution: Difference between revisions

Revision as of 12:29, 3 February 2014

In mathematics, in particular number theory, an odd 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 $D = P^{2} - 4 Q,$ such that $\gcd (N, D) = 1$ and the rank appearance of N in the sequence U(P, Q) is

\frac{1}{d} (N - (\frac{D}{N})),

where $(\frac{D}{N})$ is the Jacobi symbol.

References

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+In [[mathematics]], in particular [[number theory]], an [[odd number|odd]] [[composite number]] ''N'' is a '''Somer–Lucas ''d''-[[pseudoprime]]''' (with given ''d''&nbsp;≥&nbsp;1) if there exists a nondegenerate [[Lucas sequence]] <math>U(P,Q)</math> with the discriminant <math>D=P^2-4Q,</math> such that <math>\gcd(N,D)=1</math> and the rank appearance of ''N'' in the sequence ''U''(''P'',&nbsp;''Q'') is
+:<math>\frac{1}{d}\left(N-\left(\frac{D}{N}\right)\right),</math>
+where <math>\left(\frac{D}{N}\right)</math> is the [[Jacobi symbol]].
+== References ==
+* {{MathWorld |urlname=Somer-LucasPseudoprime |title=Somer–Lucas Pseudoprime}}
+* {{cite book |author=Ribenboim, P. |chapter=§2.X.D Somer-Lucas Pseudoprimes |chapter-url=http://books.google.com/books?id=72eg8bFw40kC&pg=PA131 |title=The New Book of Prime Number Records |edition=3rd ed. |place=New York |publisher=Springer-Verlag |pages=131–132 |year=1996}}
+{{Classes of natural numbers}}
+{{DEFAULTSORT:Somer-Lucas Pseudoprime}}
+[[Category:Pseudoprimes]]

Relativistic Breit–Wigner distribution: Difference between revisions

Revision as of 12:29, 3 February 2014

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