Lower bounds for the greatest prime factor of $ax^m+by^n$
Communications in Mathematics, Tome 6 (1998) no. 1, pp. 53-57 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11D61, 11D75, 11J25, 11J86
@article{COMIM_1998_6_1_a7,
     author = {Bugeaud, Yann},
     title = {Lower bounds for the greatest prime factor of $ax^m+by^n$},
     journal = {Communications in Mathematics},
     pages = {53--57},
     year = {1998},
     volume = {6},
     number = {1},
     mrnumber = {1822515},
     zbl = {1024.11019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a7/}
}
TY  - JOUR
AU  - Bugeaud, Yann
TI  - Lower bounds for the greatest prime factor of $ax^m+by^n$
JO  - Communications in Mathematics
PY  - 1998
SP  - 53
EP  - 57
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a7/
LA  - en
ID  - COMIM_1998_6_1_a7
ER  - 
%0 Journal Article
%A Bugeaud, Yann
%T Lower bounds for the greatest prime factor of $ax^m+by^n$
%J Communications in Mathematics
%D 1998
%P 53-57
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a7/
%G en
%F COMIM_1998_6_1_a7
Bugeaud, Yann. Lower bounds for the greatest prime factor of $ax^m+by^n$. Communications in Mathematics, Tome 6 (1998) no. 1, pp. 53-57. http://geodesic.mathdoc.fr/item/COMIM_1998_6_1_a7/

[1] G. D. Birkhoff, H. S. Vandiver: On the integral divisors of $a^n - b^n$. Ann. Math. 5 (1904), 173-180. | DOI | MR

[2] Y. Bugeaud: Bounds for the solutions of superelliptic equations. Compositio Math. 107 (1997), 187-219. | DOI | MR | Zbl

[3] Y. Bugeaud: On the greatest prime factor of $ax^m + by^n$. In : Number Theory (ed. by K. Gyory, A. Peto and V. T. Sos), Walter de Gruyter, Berlin - New York (1998), 115-122. | MR

[4] Y. Bugeaud: Sur le plus grand facteur premier de $ax^m + by^n$. C. R. Acad. Sci. Paris 326 (1998), 661-665. | DOI | MR

[5] Y. Bugeaud, K. Gyory: Bounds for the solutions of unit equations. Acta Arith. 74 (1996), 67-80. | MR

[6] Y. Bugeaud, K. Gyory: Bounds for the solutions of Thue-Mahler equations and norm form equations. Acta Arith. 74 (1996), 273-292. | MR

[7] K. Gyory: On the greatest prime factors of decomposable forms at integer points. Ann. Acad. Sci. Fenn. Ser. A1 4 (1979), 341-355. | MR

[8] K. Gyory P. Kiss, A. Schinzel: A note on Lucas and Lehmer sequences. Colloq. Math. 45 (1981), 75-80. | MR

[9] K. Gyory, A. Sarkozy: On prime factors of integers of the form $(ab+1)(bc+1)(ca + 1)$. Acta Arith. 79 (1997), 163-171. | MR

[10] S. V. Kotov: Ueber die maximale Norm der Idealteiler des Polynoms $ax^m +by^n$ mit den algebraischen Koeffizienten. Acta Arith. 31 (1976), 219-230. | MR

[11] K. Mahler: On the greatest prime factor of $ax^m + by^n$. Nieuw Archief voor Wisk. 3 (1953), 113-132. | MR

[12] T. N. Shorey: On the greatest prime factor of $(ax^m + by^n)$. Acta Arith. 36 (1980), 21-25. | MR

[13] T. N. Shorey A. J. van der Poorten R. Tijdeman, A. Schinzel: Applications of the Gelfond-Baker method to diophantine equations. Advances in transcendence theory, Academic Press, London and New-York 1977.

[14] T. N. Shorey, R. Tijdeman: Exponential Diophantine Equations. Cambridge University Press, Cambridge, 1986. | MR | Zbl

[15] P. Voutier: On primitive divisors of Lucas and Lehmer sequences III. Math. Proc. Cambridge Phil. Soc. 123 (1998), 407-419. | DOI | MR

[16] K. Yu, L. Hung: On binary recurrence sequences. Indag. Math. N. S. 6 (1995), 341-354. | DOI | MR | Zbl

[17] K. Zsigmondy: Zur Theorie der Potenzreste. Monatsh. Math. 3 (1892), 256-284.