On the power-free parts of consecutive integers

• Autorzy: B. M. M. de Weger , C. E. van de Woestijne
• Języki publikacji: EN

Kategorie tematyczne

• 11N37: Asymptotic results on arithmetic functions
• 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 90
• Numer: 4
• Strony: 387-395

Daty

wydano

1999

otrzymano

1998-10-23

poprawiono

1999-04-30

Twórcy

autor

B. M. M. de Weger

• Sportsingel 30, 2924 XN Krimpen aan den IJssel, The Netherlands

autor

C. E. van de Woestijne

• Mathematical Institute, Universiteit Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Bibliografia

• [1] J. Browkin and J. Brzeziński, Some remarks on the abc-conjecture, Math. Comp. 62 (1994), 931-939.
• [2] Y. Bugeaud and K. Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74 (1996), 273-292.
• [3] H. Cohen, A Course in Computational Algebraic Number Theory, 2nd ed., Springer, Berlin, 1995.
• [4] H. Darmon and L. Merel, Winding quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100.
• [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] L. J. Mordell, Diophantine Equations, Academic Press, London, 1969, 207-208.
• [7] J. Turk, Almost powers in short intervals, Arch. Math. (Basel) 43 (1984), 157-166.
• [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.