On the equation a x n - b y n = c

Jan-Hendrik Evertse

Compositio Mathematica (1982)

  • Volume: 47, Issue: 3, page 289-315
  • ISSN: 0010-437X

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Evertse, Jan-Hendrik. "On the equation $ax^n - by^n = c$." Compositio Mathematica 47.3 (1982): 289-315. <http://eudml.org/doc/89576>.

@article{Evertse1982,
author = {Evertse, Jan-Hendrik},
journal = {Compositio Mathematica},
keywords = {upper bounds; number of integral solutions; number of residue classes},
language = {eng},
number = {3},
pages = {289-315},
publisher = {Martinus Nijhoff Publishers},
title = {On the equation $ax^n - by^n = c$},
url = {http://eudml.org/doc/89576},
volume = {47},
year = {1982},
}

TY - JOUR
AU - Evertse, Jan-Hendrik
TI - On the equation $ax^n - by^n = c$
JO - Compositio Mathematica
PY - 1982
PB - Martinus Nijhoff Publishers
VL - 47
IS - 3
SP - 289
EP - 315
LA - eng
KW - upper bounds; number of integral solutions; number of residue classes
UR - http://eudml.org/doc/89576
ER -

References

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  1. [1] A. Baker: The theory of linear forms in logarithms. In: A. Baker and D.W. Masser (eds.), Transcendence theory, advances and applications, Ch. 1. Proc. Conf. Cambridge 1976, Academic Press, London. Zbl0361.10028MR498417
  2. [2] Y. Domar: On the diophantine equation |Axn - Byn| = 1, n ≽ 5. Math. Scand.2 (1954) 29-32. Zbl0056.03602
  3. [3] S. Hyyrö: Über die Gleichung axn - by'' = z und das Catalansche Problem. Ann. Ac. Scient. Fenn. Ser.A1355 (1964). Zbl0137.25705MR205925
  4. [4] W. Ljunggren: Einige Eigenschaften der Einheiten reeller quadratischer and rein biquadratischer Zahlkörper. Oslo Vid-Akad. Skrifter1 (1936) No. 12. Zbl0016.00802JFM63.0147.01
  5. [5] T. Nagell: Über einige kubischer Gleichungen mit zwei Unbestimmten. Math. Z.24 (1926) 422-447. MR1544774JFM51.0135.01
  6. [6] C.L. Siegel: Die Gleichung axn - byn = c. Math. Ann.114 (1937) 57-68. Zbl0015.38902MR1513124JFM63.0117.01

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