Geodesic
A generalization of the question of Sierpiński on geometric progressions
Journal of integer sequences, Tome 13 (2010) no. 3
In this paper we prove that there is no geometric progression that contains four distinct integers of the form $Dm^{2} + C, D,$m $\in $ N, $C = \pm 1 \pm 2, \pm $ 4.
Keywords: quadratic Diophantine equation, minimal positive solution, triangular numbers, geometric progression 
@article{JIS_2010__13_3_a5,
     author = {Luo,  Jiagui and Yuan,  Pingzhi},
     title = {A generalization of the question of {Sierpi\'nski} on geometric progressions},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {3},
     zbl = {1210.11040},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a5/}
}
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Luo,  Jiagui; Yuan,  Pingzhi. A generalization of the question of Sierpiński on geometric progressions. Journal of integer sequences, Tome 13 (2010) no. 3. http://geodesic.mathdoc.fr/item/JIS_2010__13_3_a5/