ArticleOriginal scientific text

Title

Explicit solution of a class of quartic Thue equations

Authors 1

Affiliations

  1. Department of Mathematics, University of Crete, Iraklion, Greece

Bibliography

  1. [BD] A. Baker and H. Davenport, The equations 3x²-2=y² and 8x²-7=z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
  2. [C1] J. H. E. Cohn, Eight Diophantine equations, Proc. London Math. Soc. (3) 16 (1966), 153-166.
  3. [C2] J. H. E. Cohn, The Diophantine equation y²=Dx⁴+1, J. London Math. Soc. 42 (1967), 475-476.
  4. [C3] J. H. E. Cohn, Some quartic Diophantine equations, Pacific J. Math. 26 (1968), 233-243.
  5. [C4] J. H. E. Cohn, The Diophantine equation y²=Dx⁴+1, II, Acta Arith. 28 (1975), 273-275.
  6. [C5] J. H. E. Cohn, The Diophantine equation y²=Dx⁴+1, III, Math. Scand. 42 (1978), 180-188.
  7. [M*] L. J. Mordell, Diophantine Equations, Pure Appl. Math. 30, Academic Press, London 1969.
  8. [MR] S. P. Mohanty and A. M. S. Ramasamy, The characteristic number of two simultaneous Pell's equations and its applications, Simon Stevin 59 (1985), 203-214.
  9. [N] T. Nagell, Sur quelques questions dans la théorie des corps biquadratiques, Ark. Mat. 4 (1961), 347-376.
  10. [N*] T. Nagell, Introduction to Number Theory, Chelsea, New York 1964.
  11. [PS] A. Pethő and R. Schulenberg, Effektives Lösen von Thue Gleichungen, Publ. Math. Debrecen 34 (1987), 189-196.
  12. [P] R. G. E. Pinch, Simultaneous Pellian equations, Math. Proc. Cambridge Philos. Soc. 103 (1988), 35-46.
  13. [TW] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132.
  14. [Z] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436
Pages:
271-283
Main language of publication
English
Received
1992-10-06
Accepted
1993-01-13
Published
1993
Exact and natural sciences