SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n!
Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 217-232

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

We prove that the only solutions in coprime positive integers to the equationare (x, y, z)=(n!–2, 1, 1, n), n≥3.
DOI : 10.1017/S0017089508004163
Mots-clés : 11D61, 11D72
(BUCHAREST), MIHAI CIPU; (MORELIA), FLORIAN LUCA; (STRASBOURG), MAURICE MIGNOTTE. SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n!. Glasgow mathematical journal, Tome 50 (2008) no. 2, pp. 217-232. doi: 10.1017/S0017089508004163
@article{10_1017_S0017089508004163,
     author = {(BUCHAREST), MIHAI CIPU and (MORELIA), FLORIAN LUCA and (STRASBOURG), MAURICE MIGNOTTE},
     title = {SOLUTIONS {OF} {THE} {DIOPHANTINE} {EQUATION} xy+yz+zx=n!},
     journal = {Glasgow mathematical journal},
     pages = {217--232},
     year = {2008},
     volume = {50},
     number = {2},
     doi = {10.1017/S0017089508004163},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004163/}
}
TY  - JOUR
AU  - (BUCHAREST), MIHAI CIPU
AU  - (MORELIA), FLORIAN LUCA
AU  - (STRASBOURG), MAURICE MIGNOTTE
TI  - SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n!
JO  - Glasgow mathematical journal
PY  - 2008
SP  - 217
EP  - 232
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004163/
DO  - 10.1017/S0017089508004163
ID  - 10_1017_S0017089508004163
ER  - 
%0 Journal Article
%A (BUCHAREST), MIHAI CIPU
%A (MORELIA), FLORIAN LUCA
%A (STRASBOURG), MAURICE MIGNOTTE
%T SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n!
%J Glasgow mathematical journal
%D 2008
%P 217-232
%V 50
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089508004163/
%R 10.1017/S0017089508004163
%F 10_1017_S0017089508004163

[1] 1.Bugeaud, Y.Linear forms in p-adic logarithms and the Diophantine equation (xn - 1)/(x-1) = yq, Math. Proc. Cambridge Philos. Soc. 127 (1999), 373–381. Google Scholar | DOI

[2] 2.Bugeaud, Y. and Laurent, M.Minoration effective de la distance p-adique entre puissances de nombres algébriques, J. Number Th. 61 (1996), 311–342. Google Scholar | DOI

[3] 3. F. Luca, M. Mignotte and Y. Roy, On the equation . Glasgow. Math. J. (2000), 351–357. Google Scholar

Cité par Sources :