Geodesic
An exponential diophantine equation related to odd perfect numbers
Tomohiro Yamada1 ; Tomohiro Yamada
1Center for Japanese language and culture, Osaka University, Osaka, Japan
Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 2, pp. 145-155 
Tomohiro Yamada; Tomohiro Yamada. An exponential diophantine equation related to odd perfect numbers. Acta mathematica Universitatis Comenianae, Tome 90 (2021) no. 2, pp. 145-155. http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a1/
@article{AMUC_2021_90_2_a1,
     author = {Tomohiro Yamada and Tomohiro Yamada},
     title = { An exponential diophantine equation related to odd perfect numbers},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {145--155},
     year = {2021},
     volume = {90},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a1/}
}
TY  - JOUR
AU  - Tomohiro Yamada
AU  - Tomohiro Yamada
TI  - An exponential diophantine equation related to odd perfect numbers
JO  - Acta mathematica Universitatis Comenianae
PY  - 2021
SP  - 145
EP  - 155
VL  - 90
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a1/
ID  - AMUC_2021_90_2_a1
ER  - 
%0 Journal Article
%A Tomohiro Yamada
%A Tomohiro Yamada
%T An exponential diophantine equation related to odd perfect numbers
%J Acta mathematica Universitatis Comenianae
%D 2021
%P 145-155
%V 90
%N 2
%U http://geodesic.mathdoc.fr/item/AMUC_2021_90_2_a1/
%F AMUC_2021_90_2_a1

Voir la notice de l'article provenant de la source Comenius University

We shall show that, for any given primes $\ell\geq 17$ and $p, q\equiv 1\pmod{\ell}$, the diophantine equation $(x^\ell-1)/(x-1)=p^m q$ has at most four positive integral solutions $(x, m)$ and give its application to odd perfect number problem.