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

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.

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.

Received:
Published online:
DOI: 10.5802/jtnb.740
Florian Luca 1; Diego Marques 2

1 Instituto de Matemáticas Universidad Nacional Autónoma de México C.P. 58089, Morelia, Michoacán, México
2 Departamento de Matemática Universidade de Brasília Brasília, DF, Brazil
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Florian Luca; Diego Marques. Perfect powers in the summatory function of the power tower. Journal de Théorie des Nombres de Bordeaux, Volume 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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