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Sep 28, 2013 at 19:07 history edited Lucia CC BY-SA 3.0
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Sep 28, 2013 at 18:54 history edited Lucia CC BY-SA 3.0
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S Sep 28, 2013 at 13:45 history suggested Michael Zieve CC BY-SA 3.0
Changed a strict inequality "<" (which was false) to "<=".
Sep 28, 2013 at 13:41 review Suggested edits
S Sep 28, 2013 at 13:45
Sep 28, 2013 at 4:53 history edited Lucia CC BY-SA 3.0
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Sep 28, 2013 at 4:12 history edited Lucia CC BY-SA 3.0
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Sep 28, 2013 at 4:01 comment added Lucia You're right. So the structure theorem I referred to gives here that the odd numbers 1, 3, 11 are three numbers out of the progression 11, 13, 1, 3; and the even numbers 0, 2, 6 are three out of the progression 0, 2, 4, 6. So a result of that type is perhaps the best you could get.
Sep 28, 2013 at 3:56 comment added Binzhou Xia Dear Lucia: Thank you so much for the wonderful references! I also believe that a good start may be when $l$ is prime. But it appears that $k$ can be values other than $1$ and $l$. For example $S=\{0,1,2,3,6,11\}$ when $l=7$.
Sep 28, 2013 at 0:38 history answered Lucia CC BY-SA 3.0