Geodesic
On D. J. Lewis's Equation x 3+117y 3 = 5
Canadian mathematical bulletin, Tome 14 (1971) no. 1, p. 111

Voir la notice de l'article provenant de la source Cambridge University Press

In a recent publication [2], D. J. Lewis stated that the Diophantine equation x 3+117y 3 = 5 has at most 18 integer solutions, but the exact number is unknown. In this paper we shall solve this problem by proving the followingTheorem. The equationx 3+117y 3 = 5 has no integer solutions. 
Finkelstein, R.; London, H. On D. J. Lewis's Equation x 3+117y 3 = 5. Canadian mathematical bulletin, Tome 14 (1971) no. 1, p. 111. doi: 10.4153/CMB-1971-020-x
@article{10_4153_CMB_1971_020_x,
     author = {Finkelstein, R. and London, H.},
     title = {On {D.} {J.} {Lewis's} {Equation} x 3+117y 3 = 5},
     journal = {Canadian mathematical bulletin},
     pages = {111--111},
     year = {1971},
     volume = {14},
     number = {1},
     doi = {10.4153/CMB-1971-020-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-020-x/}
}
TY  - JOUR
AU  - Finkelstein, R.
AU  - London, H.
TI  - On D. J. Lewis's Equation x 3+117y 3 = 5
JO  - Canadian mathematical bulletin
PY  - 1971
SP  - 111
EP  - 111
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-020-x/
DO  - 10.4153/CMB-1971-020-x
ID  - 10_4153_CMB_1971_020_x
ER  - 
%0 Journal Article
%A Finkelstein, R.
%A London, H.
%T On D. J. Lewis's Equation x 3+117y 3 = 5
%J Canadian mathematical bulletin
%D 1971
%P 111-111
%V 14
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1971-020-x/
%R 10.4153/CMB-1971-020-x
%F 10_4153_CMB_1971_020_x

[1] 1. Delone, B. N. and Faddeev, D. K., The theory of irrationalities of the third degree, Amer. Math. Soc, Providence, R.I., 1964. Google Scholar

[2] 2. LeVeque, W. J., Studies in number theory, Math. Assoc, of America, Washington, D.C., 1969. Google Scholar

[3] 3. Selmer, E. S., The Diophantine Equation ax3+ by3 + cz3 =0, Acta Math. 85 (1951), 203-362. Google Scholar

Cité par Sources :