Geodesic
An exponential Diophantine equation on triangular numbers
Mathematica Applicanda, Tome 51 (2023) no. 1, pp. 99-107.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Looking to the two remarkable identities concerning triangular numbers T_{n+1} − T_{n} = n + 1 and T^2_ {n+1} − T^2_n = (n + 1)^3 , we can extend these equations to the exponential Diophantine equation T^x_{n+1} − T^x_n = (n + 1)^y for some positive integers x, y. In this paper, we show that the above equation has only the solutions (x, y) = (1, 1) or (2, 3).
DOI : 10.14708/ma.v51i1.7196
Classification : 11D61 , 11B39
Mots-clés : Exponential Diophantine equation, Triangular numbers 
@article{10_14708_ma_v51i1_7196,
     author = {Abdelkader Hamtat},
     title = {An exponential {Diophantine} equation on triangular numbers},
     journal = {Mathematica Applicanda},
     pages = { 99--107},
     publisher = {mathdoc},
     volume = {51},
     number = {1},
     year = {2023},
     doi = {10.14708/ma.v51i1.7196},
     language = {pl},
     url = {http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7196/}
}
TY  - JOUR
AU  - Abdelkader Hamtat
TI  - An exponential Diophantine equation on triangular numbers
JO  - Mathematica Applicanda
PY  - 2023
SP  -  99
EP  - 107
VL  - 51
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7196/
DO  - 10.14708/ma.v51i1.7196
LA  - pl
ID  - 10_14708_ma_v51i1_7196
ER  - 
%0 Journal Article
%A Abdelkader Hamtat
%T An exponential Diophantine equation on triangular numbers
%J Mathematica Applicanda
%D 2023
%P  99-107
%V 51
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7196/
%R 10.14708/ma.v51i1.7196
%G pl
%F 10_14708_ma_v51i1_7196
Abdelkader Hamtat. An exponential Diophantine equation on triangular numbers. Mathematica Applicanda, Tome 51 (2023) no. 1, pp.  99-107. doi : 10.14708/ma.v51i1.7196. http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7196/

Cité par Sources :