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Sep 17, 2017 at 18:13 comment added Trevor J Richards Hah, that is a pretty compelling example Matt F.
Dec 29, 2013 at 20:57 history bounty ended Dirk
Dec 29, 2013 at 11:06 comment added user44143 Dirk, happy to answer any questions. For what it's worth, you can check that, e.g. $p$ behaves appropriately in @Mark Sapir's example, with $k=51654$, $q=250000 \left(1-\frac{1}{4} \left(x-\frac{1}{5}\right)^2\right)^{3k} (x-1/2)^2(x-1/3)^2(x-1/4)^2+921600 \left(1-\frac{1}{4} \left(x-\frac{1}{4}\right)^2\right)^{3k} (x-1/2)^2(x-1/3)^2(x-1/5)^2-291600 \left(1-\frac{1}{4} \left(x-\frac{1}{3}\right)^2\right)^{3k}(x-1/2)^2(x-1/4)^2(x-1/5)^2-6400 \left(1-\frac{1}{4} \left(x-\frac{1}{2}\right)^2\right)^{3k} (x-1/3)^2 (x-1/4)^2 (x-1/5)^2$.
Dec 26, 2013 at 17:28 vote accept Dirk
Dec 26, 2013 at 17:28 comment added Dirk That looks very interesting! Christmas time prevents that I check the answer in detail right now and since I am not sure, if I am going to come back here in due time I check this answer as correct right now to cash the bounty. Maybe I'll come back with questions later.
Dec 24, 2013 at 17:15 history edited user44143 CC BY-SA 3.0
replaced n by N and clarified
Dec 24, 2013 at 17:12 review Late answers
Dec 24, 2013 at 17:27
Dec 24, 2013 at 16:54 history answered user44143 CC BY-SA 3.0