Sur l’équation diophantienne y 2 =x 3 +k

Avec les contributions de : Baker

Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 16 (1974-1975) no. 2, Exposé no. G14, 8 p. 
@article{SDPP_1974-1975__16_2_A13_0,
     author = {Moulin, Herv\'e},
     title = {Sur l{\textquoteright}\'equation diophantienne $y^2 = x^3 + k$},
     journal = {S\'eminaire Delange-Pisot-Poitou. Th\'eorie des nombres},
     note = {talk:G14},
     pages = {G1--G8},
     publisher = {Secr\'etariat math\'ematique},
     volume = {16},
     number = {2},
     year = {1974-1975},
     mrnumber = {404131},
     zbl = {0319.10018},
     language = {fr},
     url = {http://www.numdam.org/item/SDPP_1974-1975__16_2_A13_0/}
}
TY  - JOUR
AU  - Moulin, Hervé
TI  - Sur l’équation diophantienne $y^2 = x^3 + k$
JO  - Séminaire Delange-Pisot-Poitou. Théorie des nombres
N1  - talk:G14
PY  - 1974-1975
SP  - G1
EP  - G8
VL  - 16
IS  - 2
PB  - Secrétariat mathématique
UR  - http://www.numdam.org/item/SDPP_1974-1975__16_2_A13_0/
LA  - fr
ID  - SDPP_1974-1975__16_2_A13_0
ER  - 
%0 Journal Article
%A Moulin, Hervé
%T Sur l’équation diophantienne $y^2 = x^3 + k$
%J Séminaire Delange-Pisot-Poitou. Théorie des nombres
%Z talk:G14
%D 1974-1975
%P G1-G8
%V 16
%N 2
%I Secrétariat mathématique
%U http://www.numdam.org/item/SDPP_1974-1975__16_2_A13_0/
%G fr
%F SDPP_1974-1975__16_2_A13_0
Moulin, Hervé. Sur l’équation diophantienne $y^2 = x^3 + k$. Séminaire Delange-Pisot-Poitou. Théorie des nombres, Tome 16 (1974-1975) no. 2, Exposé no. G14, 8 p. http://www.numdam.org/item/SDPP_1974-1975__16_2_A13_0/

[1] Atkin (A.O.L.) and Birch (B.J.) [Editors]. - Computers in number theory. Proceedings of the Atlas symposium [2. 1969. Oxford]. - London and New York, Academic Press, 1971. | MR | Zbl

[2] Baker (A.). - Contribution to the theory of diophantine equations, Phil. Trans. Royal Soc. London, Series A, t. 263, 1969, p. 173-208. | Zbl

[3] Baker (A.). - The diophantine equation y2 = ax3 + bx2 + cx + d , J. London math. Soc., t. 43, 1968, p. 1-9. | MR | Zbl

[4] Baker (A.). - Linear forms in the logarithm of algebraic numbers, II., Mathematika, London, t. 14, 1967, p. 220-228. | MR | Zbl

[5] Baker (A.). - Linear forms in the logarithm of algebraic numbers , IV., Mathematika, London, t. 15, 1968, p. 204-216. | MR | Zbl

[6] Borevič (Z.I.) and Safarevič (I.R.). - Number theory. Translated from the russian. - New York, Academic Press, 1966 (Pure and applied Mathematics, Academic Press, 20). | MR | Zbl

[7] Dickson (L.E.). - History of the theory of numbers, Vol. 2. - Washington, Carnegie Institution of Washington, 1920.

[8] Hemer (O.). - Notes on the diophantine equation y2 - k = x3 , Arkiv för Mat., t. 3, 1954, p. 67-77. | MR | Zbl

[9] Lang (S.). - Transcendental numbers and diophantine approximations, Bull. Amer, math. Soc., t. 77, 1971, p. 635-677. | MR | Zbl

[10] Mignotte (M.). - Amélioration effective du théorème de Liouville, Séminaire Delange-Pisot-Poitou : Théorie des nombres, 15e année, 1973/74, n° G4, 5 p. | Numdam | Zbl

[11] Mordell (L.J.). - Note on the integer solutions of the equation Ey2 = Ax3 + Bx2 + Cx + D , Messenger Math., t. 51, 1921, p. 169-171. | JFM

[12] Mordell (L.J.). - Diophantine equations. - London, New York, Academic Press, 1969 (Pure and applied Mathematics, Academic Press, 30). | MR | Zbl

[13] Serre (J.-P.). - Cours d'arithmétique. - Paris, Presses Universitaires de France, 1970 (Collection SUP. "Le Mathématicien", 2). | MR | Zbl

[14] Stark (H.M.). - Effective estimates of solutions of some diophantine equations, Acta Arithm., Warszawa, t. 24, 1973, p. 251-259. | MR | Zbl

[15] Thue (A.). - Über Annäherungswerte algebraischer Zahlen J. reine und angew. Math., t. 135, 1909, p. 284-305. | JFM

[16] Weil (A.). - Sur les courbes algébriques et les variétés qui s'en déduisent. - Paris, Hermann, 1948 (Act. scient, et Ind., 1041 ; Publ. Inst. Math. Univ. Strasbourg, 7). | MR | Zbl