Geodesic
On an additive problem with squarefree numbers
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 41-47

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An asymptotic formula for the number of representations of a positive integer $N$ in the form $q_1+q_2+[\alpha q_3]$ is obtained, where $q_1$, $q_2$, $q_3$ are squarefree numbers and $\alpha>1$ is a fixed irrational algebraic number. 
@article{ISU_2013_13_4_a4,
     author = {D. V. Goryashin},
     title = {On an additive problem with squarefree numbers},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {41--47},
     publisher = {mathdoc},
     volume = {13},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a4/}
}
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D. V. Goryashin. On an additive problem with squarefree numbers. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 4, pp. 41-47. http://geodesic.mathdoc.fr/item/ISU_2013_13_4_a4/