On the power-free parts of consecutive integers

B. M. M. de Weger; C. E. van de Woestijne

Acta Arithmetica (1999)

  • Volume: 90, Issue: 4, page 387-395
  • ISSN: 0065-1036

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B. M. M. de Weger, and C. E. van de Woestijne. "On the power-free parts of consecutive integers." Acta Arithmetica 90.4 (1999): 387-395. <http://eudml.org/doc/207335>.

@article{B1999,
author = {B. M. M. de Weger, C. E. van de Woestijne},
journal = {Acta Arithmetica},
keywords = {consecutive integers; solutions of Thue equations; Baker's theory},
language = {eng},
number = {4},
pages = {387-395},
title = {On the power-free parts of consecutive integers},
url = {http://eudml.org/doc/207335},
volume = {90},
year = {1999},
}

TY - JOUR
AU - B. M. M. de Weger
AU - C. E. van de Woestijne
TI - On the power-free parts of consecutive integers
JO - Acta Arithmetica
PY - 1999
VL - 90
IS - 4
SP - 387
EP - 395
LA - eng
KW - consecutive integers; solutions of Thue equations; Baker's theory
UR - http://eudml.org/doc/207335
ER -

References

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  1. [1] J. Browkin and J. Brzeziński, Some remarks on the abc-conjecture, Math. Comp. 62 (1994), 931-939. Zbl0804.11006
  2. [2] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292. Zbl0861.11024
  3. [3] H. Cohen, A Course in Computational Algebraic Number Theory, 2nd ed., Springer, Berlin, 1995. 
  4. [4] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100. Zbl0976.11017
  5. [5] M. Langevin, Cas d'égalité pour le Théorème de Mason et applications de la conjecture (abc), C. R. Acad. Sci. Paris Sér. I 317 (1993), 441-444. 
  6. [6] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969, 207-208. 
  7. [7] J. Turk, Almost powers in short intervals, Arch. Math. (Basel) 43 (1984), 157-166. Zbl0524.10037
  8. [8] B. M. M. de Weger and C. E. van de Woestijne, On the diameter of sets of almost powers, Acta Arith., this issue, 371-385. Zbl0971.11050

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