ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Ist. Univ. Arch. D.S.T.R., S. Croce, 191, 30135 Venezia, Italy

Bibliography

  1. [CT] J.-L. Colliot-Thélène, Letter to T. Ekedahl, 9/21/1988, unpublished.
  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.
  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.
  6. [Ho] C. Hooley, On Artin's conjecture, J. Reine Angew. Math. 225 (1967), 209-220.
  7. [La] S. Lang, Fundamentals of Diophantine Geometry, Springer, 1983.
  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).
  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.
Pages:
153-164
Main language of publication
English
Received
1996-02-12
Accepted
1996-07-02
Published
1996
Exact and natural sciences