Perfect powers in the summatory function of the power tower
Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 703-718.

Soit (a n ) n1 la suite donnée par a 1 =1 et a n =n a n-1 pour n2. Dans cet article, on montre que la seule solution de l’équation

a1++an=ml

avec des entiers positifs l>1,m et n est m=n=1.

Let (a n ) n1 be the sequence given by a 1 =1 and a n =n a n-1 for n2. In this paper, we show that the only solution of the equation

a1++an=ml

is in positive integers l>1,m and n is m=n=1.

Reçu le :
Publié le :
DOI : https://doi.org/10.5802/jtnb.740
@article{JTNB_2010__22_3_703_0,
     author = {Florian Luca and Diego Marques},
     title = {Perfect powers in the summatory function of the power tower},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {703--718},
     publisher = {Universit\'e Bordeaux 1},
     volume = {22},
     number = {3},
     year = {2010},
     doi = {10.5802/jtnb.740},
     zbl = {1231.11040},
     mrnumber = {2769339},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.740/}
}
Florian Luca; Diego Marques. Perfect powers in the summatory function of the power tower. Journal de Théorie des Nombres de Bordeaux, Tome 22 (2010) no. 3, pp. 703-718. doi : 10.5802/jtnb.740. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.740/

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