Geodesic
Catalanova domněnka dokázána
Pokroky matematiky, fyziky a astronomie, Tome 50 (2005) no. 4, pp. 280-285
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 11D61, 11R18, 11Y50 
@article{PMFA_2005_50_4_a2,
     author = {Bugeaud, Yann and Mignotte, Maurice},
     title = {Catalanova domn\v{e}nka dok\'az\'ana},
     journal = {Pokroky matematiky, fyziky a astronomie},
     pages = {280--285},
     year = {2005},
     volume = {50},
     number = {4},
     language = {cs},
     url = {http://geodesic.mathdoc.fr/item/PMFA_2005_50_4_a2/}
}
TY  - JOUR
AU  - Bugeaud, Yann
AU  - Mignotte, Maurice
TI  - Catalanova domněnka dokázána
JO  - Pokroky matematiky, fyziky a astronomie
PY  - 2005
SP  - 280
EP  - 285
VL  - 50
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/PMFA_2005_50_4_a2/
LA  - cs
ID  - PMFA_2005_50_4_a2
ER  - 
%0 Journal Article
%A Bugeaud, Yann
%A Mignotte, Maurice
%T Catalanova domněnka dokázána
%J Pokroky matematiky, fyziky a astronomie
%D 2005
%P 280-285
%V 50
%N 4
%U http://geodesic.mathdoc.fr/item/PMFA_2005_50_4_a2/
%G cs
%F PMFA_2005_50_4_a2
Bugeaud, Yann; Mignotte, Maurice. Catalanova domněnka dokázána. Pokroky matematiky, fyziky a astronomie, Tome 50 (2005) no. 4, pp. 280-285. http://geodesic.mathdoc.fr/item/PMFA_2005_50_4_a2/

[1] Bilu, Yu.: Catalan’ conjecture (after Mihăilescu). Sém. Bourbaki, 55 ème année, 909, 2002/03, 24 s.

[2] Bugeaud, Y., Hanrot, G.: Un noveau critère pour l’équation de Catalan. Mathematika 47 (2000), 63–73. | MR

[3] Cassels, J. W. S.: On the equation $a^x-b^y=1$, II. Proc. Cambridge Philos. Soc. 56 (1960), 97–103. | MR

[4] Inkeri, K.: On Catalan’s problem. Acta Arith. 9 (1964), 285–290. | MR | Zbl

[5] Inkeri, K.: On Catalan’s conjecture. J. Number Theory 34 (1990), 142–152. | MR | Zbl

[6] Ko Chao: On the diophantine equation ${x^2=y^n+1}$, ${xy\ne 0}$. Sci. Sinica 14 (1965), 457–460. | MR

[7] Langevin, M.: Quelques applications de nouveaux résultats de van der Poorten. Sém. Delange-Pisot-Poitou, 1977/78, Paris, Exp. 4, 7 s. | MR | Zbl

[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.

[9] Metsänkylä, T.: Catalan’s conjecture: another old Diophantine problem solved. Bull. Amer. Math. Soc. (N. S.) 41 (2004), 43–57. | MR

[10] Mignotte, M.: A criterion on Catalan equation. J. Number Theory 52 (1995), 280–284. | MR

[11] Mignotte, M.: Catalan’s equation just before 2000. Number theory (Turku, 1999), 247–254, de Gruyter, Berlin 2001. | MR

[12] Mihăilescu, P.: A class number free criterion for Catalan’s conjecture. J. Number Theory 99 (2003), 225–231.

[13] Mihăilescu, P.: Primary cyclotomic units and a proof of Catalan’s conjecture. J. Reine Angew. Math. 572 (2004), 167–195. | MR

[14] Ribenboim, P.: Catalan’s conjecture. Academic Press, Boston 1994. | MR | Zbl

[15] Schwarz, W.: A note on Catalan equation. Acta Arith. 72 (1995), 277–279. | MR

[16] Tijdeman, R.: On the equation of Catalan. Acta Arith. 29 (1976), 197–209. | MR