A Quick Proof of Sprindzhuk’s Decomposition Theorem

  • Yuri F. Bilu
  • David Masser
Part of the Bolyai Society Mathematical Studies book series (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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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2006

Authors and Affiliations

  • Yuri F. Bilu
    • 1
  • David Masser
    • 2
  1. 1.Institute of MathematicsUniversity of Bordeaux 1TalenceFrance
  2. 2.Department of MathematicsUniversity of BaselBaselSwitzerland

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