| Title:
|
Catalanova domněnka dokázána (Czech) |
| Title:
|
Catalan's conjecture proved (English) |
| Author:
|
Bugeaud, Yann |
| Author:
|
Mignotte, Maurice |
| Language:
|
Czech |
| Journal:
|
Pokroky matematiky, fyziky a astronomie |
| ISSN:
|
0032-2423 |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2005 |
| Pages:
|
280-285 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11D61 |
| MSC:
|
11R18 |
| MSC:
|
11Y50 |
| Note:
|
Z anglického rukopisu přeložil M. Klazar. (Czech) |
| Note:
|
From the English manuscript translated by M. Klazar. (English) |
| . |
| Date available:
|
2010-12-11T21:14:52Z |
| Last updated:
|
2012-08-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141281 |
| . |
| Reference:
|
[1] Bilu, Yu.: Catalan’ conjecture (after Mihăilescu).Sém. Bourbaki, 55 ème année, 909, 2002/03, 24 s. |
| Reference:
|
[2] Bugeaud, Y., Hanrot, G.: Un noveau critère pour l’équation de Catalan.Mathematika 47 (2000), 63–73. MR 1924488 |
| Reference:
|
[3] Cassels, J. W. S.: On the equation $a^x-b^y=1$, II.Proc. Cambridge Philos. Soc. 56 (1960), 97–103. MR 0114791 |
| Reference:
|
[4] Inkeri, K.: On Catalan’s problem.Acta Arith. 9 (1964), 285–290. Zbl 0127.27102, MR 0168518 |
| Reference:
|
[5] Inkeri, K.: On Catalan’s conjecture.J. Number Theory 34 (1990), 142–152. Zbl 0699.10029, MR 1042488 |
| Reference:
|
[6] Ko Chao: On the diophantine equation ${x^2=y^n+1}$, ${xy\ne 0}$.Sci. Sinica 14 (1965), 457–460. MR 0183684 |
| Reference:
|
[7] Langevin, M.: Quelques applications de nouveaux résultats de van der Poorten.Sém. Delange-Pisot-Poitou, 1977/78, Paris, Exp. 4, 7 s. Zbl 0354.10008, MR 0498426 |
| Reference:
|
[8] Lebesgue, V. A.: Sur l’impossibilité en nombres entiers de l’équation ${x^m=y^2+1}$.Nouv. Ann. Math. 9 (1850), 178–181. |
| Reference:
|
[9] Metsänkylä, T.: Catalan’s conjecture: another old Diophantine problem solved.Bull. Amer. Math. Soc. (N. S.) 41 (2004), 43–57. MR 2015449 |
| Reference:
|
[10] Mignotte, M.: A criterion on Catalan equation.J. Number Theory 52 (1995), 280–284. MR 1336750 |
| Reference:
|
[11] Mignotte, M.: Catalan’s equation just before 2000.Number theory (Turku, 1999), 247–254, de Gruyter, Berlin 2001. MR 1822013 |
| Reference:
|
[12] Mihăilescu, P.: A class number free criterion for Catalan’s conjecture.J. Number Theory 99 (2003), 225–231. |
| Reference:
|
[13] Mihăilescu, P.: Primary cyclotomic units and a proof of Catalan’s conjecture.J. Reine Angew. Math. 572 (2004), 167–195. MR 2076124 |
| Reference:
|
[14] Ribenboim, P.: Catalan’s conjecture.Academic Press, Boston 1994. Zbl 0824.11010, MR 1259738 |
| Reference:
|
[15] Schwarz, W.: A note on Catalan equation.Acta Arith. 72 (1995), 277–279. MR 1347490 |
| Reference:
|
[16] Tijdeman, R.: On the equation of Catalan.Acta Arith. 29 (1976), 197–209. MR 0404137 |
| . |
