Geodesic
Insolvability of
Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 167-169

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

DOI

A number of interesting Diophantine equations are of the a form f(n) = f(a) f(b). Thus the case f(a) = aa has been studied by C. Ko [2] and W. H. Mills [3] and a class of non-trivial solutions has been found, though whether these give all the solutions is still unsettled. The case f(n) = n! has been mentioned by W. Sierpinski. Here the situation is that besides the trivial solutions m! = m! 1! and (m!-1)! m! = (m!)! and the special solution 10! =7! 6! no other solutions are known, nor are they known not to exist. In the present note we show that the equation in the title has no solutions. A sketch of a somewhat different proof that this equation has at most a finite number of solutions was recently communicated to the author by P. Erdös. 
Moser, L. Insolvability of. Canadian mathematical bulletin, Tome 6 (1963) no. 2, pp. 167-169. doi: 10.4153/CMB-1963-015-6
@article{10_4153_CMB_1963_015_6,
     author = {Moser, L.},
     title = {Insolvability of},
     journal = {Canadian mathematical bulletin},
     pages = {167--169},
     year = {1963},
     volume = {6},
     number = {2},
     doi = {10.4153/CMB-1963-015-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-015-6/}
}
TY  - JOUR
AU  - Moser, L.
TI  - Insolvability of
JO  - Canadian mathematical bulletin
PY  - 1963
SP  - 167
EP  - 169
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-015-6/
DO  - 10.4153/CMB-1963-015-6
ID  - 10_4153_CMB_1963_015_6
ER  - 
%0 Journal Article
%A Moser, L.
%T Insolvability of
%J Canadian mathematical bulletin
%D 1963
%P 167-169
%V 6
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1963-015-6/
%R 10.4153/CMB-1963-015-6
%F 10_4153_CMB_1963_015_6

Cité par Sources :