Michael Filaseta

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We address conjectures of P. Erd˝ os and conjectures of Y.-G. Chen concerning the numbers in the title. We obtain a variety of related results, including a new smallest positive integer that is simultaneously a Sierpi´nski number and a Riesel number and a proof that for every positive integer r, there is an integer k such that the numbers k, k 2 , k 3 ,. ..(More)
An algorithm is described that determines whether a given polynomial with integer coefficients has a cyclotomic factor. The algorithm is intended to be used for sparse polynomials given as a sequence of coefficient-exponent pairs. A running analysis shows that, for a fixed number of nonzero terms, the algorithm runs in polynomial time.
Nous répondonsà trois questions concernant la réducti-bilité (ou irréductibilité) de 0, 1-polynômes, polynômes qui n'ont pour seuls coefficients que 0 ou 1. Lapremì ere question est de déterminer si une suite de polynômes qui se présente naturellement est finie.Deuxì emement, nous discutons si tout sous-ensemble fini d'un ensemble infini de nombres entiers(More)