Perfect powers in arithmetical progression (II)

T. N. Shorey; R. Tijdeman

Compositio Mathematica (1992)

  • Volume: 82, Issue: 1, page 107-117
  • ISSN: 0010-437X

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Shorey, T. N., and Tijdeman, R.. "Perfect powers in arithmetical progression (II)." Compositio Mathematica 82.1 (1992): 107-117. <http://eudml.org/doc/90144>.

@article{Shorey1992,
author = {Shorey, T. N., Tijdeman, R.},
journal = {Compositio Mathematica},
keywords = {perfect powers; arithmetical progression; exponential diophantine equation; least prime factor; greatest prime factor; greatest square free factor},
language = {eng},
number = {1},
pages = {107-117},
publisher = {Kluwer Academic Publishers},
title = {Perfect powers in arithmetical progression (II)},
url = {http://eudml.org/doc/90144},
volume = {82},
year = {1992},
}

TY - JOUR
AU - Shorey, T. N.
AU - Tijdeman, R.
TI - Perfect powers in arithmetical progression (II)
JO - Compositio Mathematica
PY - 1992
PB - Kluwer Academic Publishers
VL - 82
IS - 1
SP - 107
EP - 117
LA - eng
KW - perfect powers; arithmetical progression; exponential diophantine equation; least prime factor; greatest prime factor; greatest square free factor
UR - http://eudml.org/doc/90144
ER -

References

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  1. 1 A. Baker, A sharpening of the bounds for linear forms in logarithms I, Acta Arith.21, 117-129 (1972). Zbl0244.10031MR302573
  2. 2 P. Dénes, Über die Diophantische Gleichung xl + yl = czl, Acta Math.88, 241-251 (1952). Zbl0048.27503MR68560
  3. 3 P. Erdös, Note on the product of consecutive integers (II), J. London Math. Soc.14, 245-249 (1939). Zbl0026.38801MR240JFM65.1145.01
  4. 4 J.-H. Evertse, On the equation axn - byn = c, Compositio Math. 47, 289-315 (1982). Zbl0498.10014MR681611
  5. 5 G. Faltings, Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math.71, 349-366 (1983). Zbl0588.14026MR718935
  6. 6 N.I. Feldman, An effective sharpening of the exponent in Liouville's theorem (Russian), Izv. Akad. Nauk SSSR Ser. mat.35, 973-990 (1971, English trans.: Math. USSR Izv.5, 985-1002. Zbl0259.10031MR289418
  7. 7 J. Mueller, Counting solutions of |axr - byr| ≤ h, Quart. J. Math. Oxford (2), 38, 503-513 (1987). Zbl0632.10014
  8. 8 L.J. Mordell, Diophantine Equations, Academic Press, London (1969). Zbl0188.34503MR249355
  9. 9 T.N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Mathematics87 (1986). Zbl0606.10011MR891406
  10. 10 T.N. Shorey and R. Tijdeman, Perfect powers in arithmetical progression, J. Madras Univ., Section B, 51, 173-180 (1988). Zbl1194.11046
  11. 11 T.N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Comp. Math.75, 307-344 (1990). Zbl0708.11021MR1070417
  12. 12 W. Wei, On the least prime in an arithmetic progression, Acta Math. Sinica29, 826-836 (1986) Zbl0621.10029MR888852

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