On consecutive integers of the form ax², by² and cz²

Michael A. Bennett

Acta Arithmetica (1999)

  • Volume: 88, Issue: 4, page 363-370
  • ISSN: 0065-1036

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Michael A. Bennett. "On consecutive integers of the form ax², by² and cz²." Acta Arithmetica 88.4 (1999): 363-370. <http://eudml.org/doc/207253>.

@article{MichaelA1999,
author = {Michael A. Bennett},
journal = {Acta Arithmetica},
keywords = {simultaneous Pell equations; linear forms in logarithms; lower bounds for linear forms in logarithms of algebraic numbers},
language = {eng},
number = {4},
pages = {363-370},
title = {On consecutive integers of the form ax², by² and cz²},
url = {http://eudml.org/doc/207253},
volume = {88},
year = {1999},
}

TY - JOUR
AU - Michael A. Bennett
TI - On consecutive integers of the form ax², by² and cz²
JO - Acta Arithmetica
PY - 1999
VL - 88
IS - 4
SP - 363
EP - 370
LA - eng
KW - simultaneous Pell equations; linear forms in logarithms; lower bounds for linear forms in logarithms of algebraic numbers
UR - http://eudml.org/doc/207253
ER -

References

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  1. [1] W. S. Anglin, Simultaneous Pell equations, Math. Comp. 65 (1996), 355-359. Zbl0848.11007
  2. [2] A. Baker and H. Davenport, The equations 3x² - 2 = y² and 8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137. 
  3. [3] M. A. Bennett, On the number of solutions of simultaneous Pell equations, J. Reine Angew. Math. 498 (1998), 173-199. Zbl1044.11011
  4. [4] J. H. E. Cohn, The Diophantine equation x⁴ - Dy² = 1, II, Acta Arith. 78 (1997), 401-403. Zbl0870.11018
  5. [5] A. Khintchine, Continued Fractions, 3rd ed., P. Noordhoff, Groningen, 1963. Zbl0117.28503
  6. [6] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminants d'interpolation, J. Number Theory 55 (1995), 285-321. Zbl0843.11036
  7. [7] W. Ljunggren, Litt om simultane Pellske ligninger, Norsk Mat. Tidsskr. 23 (1941), 132-138. 
  8. [8] W. Ljunggren, Über die Gleichung x⁴ - Dy² = 1, Arch. f. Math. og Naturvidenskab B 45 (1942), 61-70. Zbl68.0069.01
  9. [9] D. W. Masser and J. H. Rickert, Simultaneous Pell equations, J. Number Theory 61 (1996), 52-66. Zbl0882.11016
  10. [10] R. G. E. Pinch, Simultaneous Pellian equations, Math. Proc. Cambridge Philos. Soc. 103 (1988), 35-46. Zbl0641.10014
  11. [11] D. T. Walker, On the diophantine equation mX² - nY² = ± 1, Amer. Math. Monthly 74 (1967), 504-513. Zbl0154.29604
  12. [12] P. G. Walsh, On two classes of simultaneous Pell equations with no solutions, Math. Comp., to appear. Zbl0911.11017
  13. [13] P. G. Walsh, On integer solutions to x² - dy² = 1, z² - 2dy² = 1, Acta Arith. 82 (1997), 69-76. 

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