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A Quick Proof of Sprindzhuk’s Decomposition Theorem

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More Sets, Graphs and Numbers

Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 15))

Abstract

In [11] Sprindzhuk proved the following striking theorem. Theorem 1 (Sprindzhuk [11]). Let F(x,y) ∈ ℚ[x,y] be a ℚ-irreducible Polynomial satisfying

$$ F(0,0) = 0, \frac{{\partial F}} {{\partial y}}(0,0) \ne 0. $$
(1)

Then for all but finitely many prime numbers p, the polynomial F(p,y) is ℚ-irreducible.

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References

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Bordeaux 1, 33405, Talence, France

    Yuri F. Bilu

  2. Department of Mathematics, University of Basel, Petersplatz 1, 4003, Basel, Switzerland

    David Masser

Authors
  1. Yuri F. Bilu
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  2. David Masser
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Editor information

Editors and Affiliations

  1. Hungarian Academy of Sciences, Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    Ervin Győri  & Gyula O. H. Katona  & 

  2. Eötvös University (Budapest)/Microsoft (Seattle), Pázmány Péter sétány 1/C, 1117, Budapest, Hungary

    László Lovász

  3. Budapest University of Technology and Economics, Pázmány Péter sétány 1/D, 1117, Budapest, Hungary

    Tamás Fleiner

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Dedicated to the memory of V. G. Sprindzhuk

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© 2006 János Bolyai Mathematical Society and Springer Verlag

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Bilu, Y.F., Masser, D. (2006). A Quick Proof of Sprindzhuk’s Decomposition Theorem. In: Győri, E., Katona, G.O.H., Lovász, L., Fleiner, T. (eds) More Sets, Graphs and Numbers. Bolyai Society Mathematical Studies, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32439-3_2

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