Let be the sequence given by and for . In this paper, we show that the only solution of the equation
is in positive integers and is .
Soit la suite donnée par et pour . Dans cet article, on montre que la seule solution de l’équation
avec des entiers positifs et est .
Published online:
DOI: 10.5802/jtnb.740
Author's affiliations:
@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/} }
TY - JOUR TI - Perfect powers in the summatory function of the power tower JO - Journal de Théorie des Nombres de Bordeaux PY - 2010 DA - 2010/// SP - 703 EP - 718 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.740/ UR - https://zbmath.org/?q=an%3A1231.11040 UR - https://www.ams.org/mathscinet-getitem?mr=2769339 UR - https://doi.org/10.5802/jtnb.740 DO - 10.5802/jtnb.740 LA - en ID - JTNB_2010__22_3_703_0 ER -
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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