Geodesic
A generalization of the question of Sierpiński on geometric progressions
Journal of integer sequences, Tome 13 (2010) no. 3.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2010},
     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/