Geodesic
Perfect squares of the form $[\alpha n]$
Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 68-73

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An asymptotic formula is proved for the number of perfect squares in the sequence $[\alpha n]$ for algebraic numbers $\alpha$ and irrational numbers $\alpha$ with restricted partial quotients.
Keywords: perfect squares, Beatty sequence, asymptotic formula, exponential sums, Weyl sums. 
@article{CHEB_2013_14_2_a5,
     author = {D. V. Goryashin},
     title = {Perfect squares of the form $[\alpha n]$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {68--73},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a5/}
}
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D. V. Goryashin. Perfect squares of the form $[\alpha n]$. Čebyševskij sbornik, Tome 14 (2013) no. 2, pp. 68-73. http://geodesic.mathdoc.fr/item/CHEB_2013_14_2_a5/