| Title:
|
Lower bounds for the greatest prime factor of $ax^m+by^n$ (English) |
| Author:
|
Bugeaud, Yann |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
6 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
53-57 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11D61 |
| MSC:
|
11D75 |
| MSC:
|
11J25 |
| MSC:
|
11J86 |
| idZBL:
|
Zbl 1024.11019 |
| idMR:
|
MR1822515 |
| . |
| Date available:
|
2009-01-30T09:05:58Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120540 |
| . |
| Reference:
|
[1] G. D. Birkhoff, H. S. Vandiver: On the integral divisors of $a^n - b^n$.Ann. Math. 5 (1904), 173-180. MR 1503541, 10.2307/2007263 |
| Reference:
|
[2] Y. Bugeaud: Bounds for the solutions of superelliptic equations.Compositio Math. 107 (1997), 187-219. Zbl 0886.11016, MR 1458749, 10.1023/A:1000130114331 |
| Reference:
|
[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 1628837 |
| Reference:
|
[4] Y. Bugeaud: Sur le plus grand facteur premier de $ax^m + by^n$.C. R. Acad. Sci. Paris 326 (1998), 661-665. MR 1641722, 10.1016/S0764-4442(98)80026-8 |
| Reference:
|
[5] Y. Bugeaud, K. Gyory: Bounds for the solutions of unit equations.Acta Arith. 74 (1996), 67-80. MR 1367579 |
| Reference:
|
[6] Y. Bugeaud, K. Gyory: Bounds for the solutions of Thue-Mahler equations and norm form equations.Acta Arith. 74 (1996), 273-292. MR 1373714 |
| Reference:
|
[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 0565882 |
| Reference:
|
[8] K. Gyory P. Kiss, A. Schinzel: A note on Lucas and Lehmer sequences.Colloq. Math. 45 (1981), 75-80. MR 0652603 |
| Reference:
|
[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 1438599 |
| Reference:
|
[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 0427226 |
| Reference:
|
[11] K. Mahler: On the greatest prime factor of $ax^m + by^n$.Nieuw Archief voor Wisk. 3 (1953), 113-132. MR 0057899 |
| Reference:
|
[12] T. N. Shorey: On the greatest prime factor of $(ax^m + by^n)$.Acta Arith. 36 (1980), 21-25. MR 0576580 |
| Reference:
|
[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. |
| Reference:
|
[14] T. N. Shorey, R. Tijdeman: Exponential Diophantine Equations.Cambridge University Press, Cambridge, 1986. Zbl 0606.10011, MR 0891406 |
| Reference:
|
[15] P. Voutier: On primitive divisors of Lucas and Lehmer sequences III.Math. Proc. Cambridge Phil. Soc. 123 (1998), 407-419. MR 1607969, 10.1017/S0305004197002223 |
| Reference:
|
[16] K. Yu, L. Hung: On binary recurrence sequences.Indag. Math. N. S. 6 (1995), 341-354. Zbl 0853.11014, MR 1351152, 10.1016/0019-3577(95)93201-K |
| Reference:
|
[17] K. Zsigmondy: Zur Theorie der Potenzreste.Monatsh. Math. 3 (1892), 256-284. |
| . |
