Regular sets in residual classes
Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 224-228

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Sets regular modulo a fixed odd prime power are explicitly constructed under the condition that their cardinalities do not exceed an arbitrarily small positive power of the modulus.
@article{MZM_1998_64_2_a8,
     author = {A. A. Karatsuba},
     title = {Regular sets in residual classes},
     journal = {Matemati\v{c}eskie zametki},
     pages = {224--228},
     publisher = {mathdoc},
     volume = {64},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a8/}
}
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A. A. Karatsuba. Regular sets in residual classes. Matematičeskie zametki, Tome 64 (1998) no. 2, pp. 224-228. http://geodesic.mathdoc.fr/item/MZM_1998_64_2_a8/