Explicit solution of a class of quartic Thue equations

Nikos Tzanakis

Acta Arithmetica (1993)

  • Volume: 64, Issue: 3, page 271-283
  • ISSN: 0065-1036

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Nikos Tzanakis. "Explicit solution of a class of quartic Thue equations." Acta Arithmetica 64.3 (1993): 271-283. <http://eudml.org/doc/206550>.

@article{NikosTzanakis1993,
author = {Nikos Tzanakis},
journal = {Acta Arithmetica},
keywords = {common solutions of Pellian equations; common values of recurrence sequences; quartic Thue equations},
language = {eng},
number = {3},
pages = {271-283},
title = {Explicit solution of a class of quartic Thue equations},
url = {http://eudml.org/doc/206550},
volume = {64},
year = {1993},
}

TY - JOUR
AU - Nikos Tzanakis
TI - Explicit solution of a class of quartic Thue equations
JO - Acta Arithmetica
PY - 1993
VL - 64
IS - 3
SP - 271
EP - 283
LA - eng
KW - common solutions of Pellian equations; common values of recurrence sequences; quartic Thue equations
UR - http://eudml.org/doc/206550
ER -

References

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  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. Zbl0136.02806
  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. Zbl0191.04902
  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. Zbl0395.10025
  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. Zbl0575.10010
  9. [N] T. Nagell, Sur quelques questions dans la théorie des corps biquadratiques, Ark. Mat. 4 (1961), 347-376. Zbl0107.03202
  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. Zbl0641.10014
  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. Zbl0657.10014
  14. [Z] D. Zagier, Large integral points on elliptic curves, Math. Comp. 48 (1987), 425-436 Zbl0611.10008

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