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Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers

Shevelev, Vladimir Y García-Pulgarín, Gilberto Y Velásquez-Soto, Juan Miguel Y Castillo, John H. (2012) Overpseudoprimes, and Mersenne and Fermat Numbers as Primover Numbers. Journal Of Integer Sequences, 15 (7). pp. 1-10. ISSN 1530-7638

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We introduce a new class of pseudoprimes, that we call "overpseudoprimes to base b", which is a subclass of the strong pseudoprimes to base b. Letting |b|n denote the multiplicative order of b modulo n, we show that a composite number n is an overpseudoprime if and only if |b|d is invariant for all divisors d > 1 of n. In particular, we prove that all composite Mersenne numbers 2p - 1, where p is prime, are overpseudoprimes to base 2 and squares of Wieferich primes are overpseudoprimes to base 2. Finally, we show that some kinds of well-known numbers are "primover to base b"; i.e., they are primes or overpseudoprimes to base b.

Tipo de Elemento: Artículo
Palabras Clave: Mersenne numbers, cyclotomic cosets of 2 modulo n, order of 2 modulo n, Poulet pseudoprime, super-Poulet pseudoprime, overpseudoprime, Wieferich prime.
Asunto: Q Ciencias > QA Mathematics
Division: Facultad de Ciencias Exactas y Naturales > Programa de Licenciatura en Matemáticas > Productividad
Depósito de Usuario: John H. Castillo
Fecha Deposito: 25 Jan 2017 22:03
Ultima Modificación: 25 Jan 2017 22:04


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