Geodesic
On Sequences {ξtn (mod 1)}
Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 727-738

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J. Mycielski has conveyed to me the following problem by P. Erdös. Let {tn} be a sequence of natural numbers such that (a) Does there exist an irrational number η such that the sequence {tnη (mod 1)} is not dense in [0,1)? 
Strzelecki, E. On Sequences {ξtn (mod 1)}. Canadian mathematical bulletin, Tome 18 (1975) no. 5, pp. 727-738. doi: 10.4153/CMB-1975-127-7
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     author = {Strzelecki, E.},
     title = {On {Sequences} {\ensuremath{\xi}tn (mod 1)}},
     journal = {Canadian mathematical bulletin},
     pages = {727--738},
     year = {1975},
     volume = {18},
     number = {5},
     doi = {10.4153/CMB-1975-127-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-127-7/}
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