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Displaying 61 – 80 of 83

Primitive Lucas d-pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Colloquium Mathematicae

Let d be a fixed positive integer. A Lucas d-pseudoprime is a Lucas pseudoprime N for which there exists a Lucas sequence U(P,Q) such that the rank of appearance of N in U(P,Q) is exactly (N-ε(N))/d, where the signature ε(N) = (D/N) is given by the Jacobi symbol with respect to the discriminant D of U. A Lucas d-pseudoprime N is a primitive Lucas d-pseudoprime if (N-ε(N))/d is the maximal rank of N among Lucas sequences U(P,Q) that exhibit N as a Lucas pseudoprime. We derive...

Pruebas determinísticas de primalidad.

Pedro Berrizbeitia (2001)

Gaceta de la Real Sociedad Matemática Española

Pseudoprvočísla

Michal Křížek, Lawrence Somer (2003)

Pokroky matematiky, fyziky a astronomie

Recherches sur la divisibilité du nombre $\frac{1.2 \dots n x}{{(1.2 \dots x)}^{n}}$ par les puissances de la factorielle $1.2 \dots n$

de Polignac (1904)

Bulletin de la Société Mathématique de France

Remarks on maximum and minimum exponents in factoring

Andrzej Schinzel, Tibor Šalát (1994)

Mathematica Slovaca

Resolution of the mixed Sierpiński problem.

Helm, Louis, Moore, Phil, Samidoost, Payam, Woltman, George (2008)

Integers

Some problems in number theory that arise from group theory.

Alexander Moretó (2007)

Publicacions Matemàtiques

In this expository paper, we present several open problerns in number theory that have arisen while doing research in group theory. These problems are on arithmetical functions or partitions. Solving some of these problems would allow to solve some open problem in group theory.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].

Sophie Germain little suns

Michal Křížek, Lawrence Somer (2004)

Mathematica Slovaca

Square-free Lucas $d$ -pseudoprimes and Carmichael-Lucas numbers

Walter Carlip, Lawrence Somer (2007)

Czechoslovak Mathematical Journal

Let $d$ be a fixed positive integer. A Lucas $d$ -pseudoprime is a Lucas pseudoprime $N$ for which there exists a Lucas sequence $U (P, Q)$ such that the rank of $N$ in $U (P, Q)$ is exactly $(N - ε (N)) / d$ , where $ε$ is the signature of $U (P, Q)$ . We prove here that all but a finite number of Lucas $d$ -pseudoprimes are square free. We also prove that all but a finite number of Lucas $d$ -pseudoprimes are Carmichael-Lucas numbers.