On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture

DOI10.1016/j.jnt.2008.02.004zbMath1221.11003OpenAlexW2153972306WikidataQ123114511 ScholiaQ123114511MaRDI QIDQ958700

Mark Kozek, Carrie Finch, Michael Filaseta

Publication date: 8 December 2008

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2008.02.004

zbMATH Keywords

covering systemPolignac's conjectureRiesel numberSierpiński number

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Arithmetic progressions (11B25) Factorization; primality (11A51)

Related Items (18)

On a problem of Romanoff type ⋮ On binomial coefficients associated with Sierpi\'{n}ski and Riesel numbers ⋮ Covering systems with odd moduli ⋮ EIGHT CONSECUTIVE POSITIVE ODD NUMBERS NONE OF WHICH CAN BE EXPRESSED AS A SUM OF TWO PRIME POWERS ⋮ Primefree shifted Lucas sequences ⋮ Nonlinear Sierpiński and Riesel numbers ⋮ Composite values of shifted exponentials ⋮ Generalized Sierpiński numbers ⋮ On Cullen numbers which are both Riesel and Sierpiński numbers ⋮ On perfect and near-perfect numbers ⋮ Unnamed Item ⋮ Chen's conjecture and its generalization ⋮ Unnamed Item ⋮ Iterated Riesel and Iterated Sierpiński Numbers ⋮ Perfect power Riesel numbers ⋮ On the density of integers of the form \(2^k + p\) in arithmetic progressions ⋮ Covers of the integers with odd moduli and their applications to the forms $x^{m}-2^{n}$ and $x^{2}-F_{3n}/2$ ⋮ Covering subsets of the integers by congruences

Cites Work

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• Sur un problème concernant les nombres \(k\cdot 2^n + 1\)
• On integers of the forms \(k\pm 2^{n}\) and \(k2^{n}\pm 1\)
• On integers of the forms \(k^r-2^n\) and \(k^r2^n+1\).
• On the Equations z^m = F (x, y ) and Ax^p + By^q = Cz^r
• Unsolved problems in number theory
• Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers

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