Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1

Umberto Zannier

Acta Arithmetica (1996)

  • Volume: 78, Issue: 2, page 153-164
  • ISSN: 0065-1036

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Umberto Zannier. "Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1." Acta Arithmetica 78.2 (1996): 153-164. <http://eudml.org/doc/206939>.

@article{UmbertoZannier1996,
author = {Umberto Zannier},
journal = {Acta Arithmetica},
keywords = {integer solutions; polynomial parametrization of diophantine equations; approximation property for affine varieties},
language = {eng},
number = {2},
pages = {153-164},
title = {Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1},
url = {http://eudml.org/doc/206939},
volume = {78},
year = {1996},
}

TY - JOUR
AU - Umberto Zannier
TI - Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1
JO - Acta Arithmetica
PY - 1996
VL - 78
IS - 2
SP - 153
EP - 164
LA - eng
KW - integer solutions; polynomial parametrization of diophantine equations; approximation property for affine varieties
UR - http://eudml.org/doc/206939
ER -

References

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  2. [Ek] T. Ekedahl, An effective version of Hilbert's Irreducibility Theorem, preprint, Stockholm 1987 (see also Séminaire de Théorie des Nombres, Paris 1988-1989, Birkhäuser, 1990, 241-248). 
  3. [G-RM] R. Gupta and M. Ram Murty, A remark on Artin's conjecture, Invent. Math. 78 (1984), 127-130. Zbl0549.10037
  4. [Hart] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math. 52, Springer, New York, 1977. 
  5. [HB] D. R. Heath-Brown, Artin's conjecture for primitive roots, Quart. J. Math. Oxford 37 (1986), 27-38. Zbl0586.10025
  6. [Ho] C. Hooley, On Artin's conjecture, J. Reine Angew. Math. 225 (1967), 209-220. Zbl0221.10048
  7. [La] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983. Zbl0528.14013
  8. [Sch] A. Schinzel, Selected Topics on Polynomials, University of Michigan Press, Ann Arbor, 1982. 
  9. [Se] J. P. Serre, Topics in Galois Theory, Jones and Bartlett Publ., Boston, 1992. 
  10. [Sko] T. Skolem, Diophantische Gleichungen, Springer, 1938, reprint Chelsea, 1950. 
  11. [Sz] K. Szymiczek, On some diophantine equations connected with triangular numbers, Zeszyty Nauk. Wyż. Szkoły Ped. w Katowicach Mat. 4 (1964), 17-22 (in Polish). Zbl0900.11007
  12. [We] A. Weil, L'arithmétique sur les courbes algébriques, Acta Math. 52 (1928), 281-315 = Coll. Papers, Vol. I, 2nd printing, Springer, 1980, 11-46. 
  13. [Wei] P. J. Weinberger, On Euclidean rings of algebraic integers, in: Proc. Sympos. Pure Math. 24, Amer. Math. Soc., 1973, 321-332. 
  14. [Za] U. Zannier, Note on traces of regular differential forms, preprint, 1995. 

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