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MR2640554 11K45 (11A55 11B25 60C99)
Arnolʹd, V. I. To what extent are arithmetic progressions of fractional parts random? (Russian) Uspekhi Mat. Nauk 63 (2008), no. 2(380), 5--20; translation in Russian Math. Surveys 63 (2008), no. 2, 205–220
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