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Sep 14, 2017 at 2:09 comment added Cuize Han Nice short argument!
Sep 14, 2017 at 2:07 vote accept Cuize Han
Sep 13, 2017 at 23:23 comment added Ilya Bogdanov I'm sorry; now I'm convinced that the answer for $\alpha=1/2$ is in the affirmative; see the new part of the answer (at the top of it).
Sep 13, 2017 at 23:22 history edited Ilya Bogdanov CC BY-SA 3.0
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Sep 13, 2017 at 17:21 comment added Cuize Han Thanks for your answer! Now I see that it won't work for length smaller than half. Your negative answer suggest it is not true for any constant smaller than 1?
Sep 13, 2017 at 14:59 history answered Ilya Bogdanov CC BY-SA 3.0