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 |
| URI: | http://sired.udenar.edu.co/id/eprint/3501 |
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