On prime factors of integers of the form (ab+1)(bc+1)(ca+1)

K. Győry; A. Sárközy

Displaying similar documents to “On prime factors of integers of the form (ab+1)(bc+1)(ca+1)”

On the greatest prime factor of (ab + 1)(bc + 1)(ca + 1)

Yann Bugeaud (1998)

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Fields containing values of algebraic functions II (On a conjecture of Schinzel)

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Interpreting reflexive theories in finitely many axioms

V. Shavrukov (1997)

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For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of $\prod_{1}$ (as well as $\sum_{1}$ ) sentences π such that GB interprets ZF+π is $Σ_{3}^{0}$ -complete.

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Paul Erdős, Moshe Rosenfeld (1997)

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On the greatest prime factor of (ab + 1) (ac + 1) (bc + 1)

C. L. Stewart, R. Tijdeman (1997)

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Trevor D. Wooley (1998)

Acta Arithmetica

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Bohr compactifications of discrete structures

Joan Hart, Kenneth Kunen (1999)

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We prove the following theorem: Given a⊆ω and $1 \leq α < ω_{1}^{C K}$ , if for some $η < ℵ_{1}$ and all u ∈ WO of length η, a is $Σ_{α}^{0} (u)$ , then a is $Σ_{α}^{0}$ .We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: $Σ_{1}^{1}$ -Turing-determinacy implies the existence of $0^{}$ .

Extending real-valued functions in βκ

Alan Dow (1997)

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An Open Coloring Axiom type principle is formulated for uncountable cardinals and is shown to be a consequence of the Proper Forcing Axiom. Several applications are found. We also study dense C*-embedded subspaces of ω*, showing that there can be such sets of cardinality $c$ and that it is consistent that ω*{pis C*-embedded for some but not all p ∈ ω*.

Examples of non-shy sets

Randall Dougherty (1994)

Fundamenta Mathematicae

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Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy...

Canonical heights on the Jacobians of curves of genus 2 and the infinite descent

E. V. Flynn, N. P. Smart (1997)

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The normalizer splitting conjecture for p-compact groups

Kasper Andersen (1999)

Fundamenta Mathematicae

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Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group $W_{X}$ . We prove that for an odd prime p, the fibration $B T \to B N \to B W_{X}$ has a section, which is unique up to vertical homotopy.

Hausdorff dimension and measures on Julia sets of some meromorphic maps

Krzysztof Barański (1995)

Fundamenta Mathematicae

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We study the Julia sets for some periodic meromorphic maps, namely the maps of the form $f (z) = h (e x p \frac{2 π i}{T} z)$ where h is a rational function or, equivalently, the maps $˜ f (z) = e x p (\frac{2 π i}{h} (z))$ . When the closure of the forward orbits of all critical and asymptotic values is disjoint from the Julia set, then it is hyperbolic and it is possible to construct the Gibbs states on J(˜f) for -α log |˜˜f|. For ˜α = HD(J(˜f)) this state is equivalent to the ˜α-Hausdorff measure or to the ˜α-packing measure provided ˜α is greater or smaller...