My favourite combinatorics problem of the day :)

Discrete Mathematics Level pending

Find all integers n ≥ 2 in the set {1,2,3...2014} for which there exist integers x1, x2, . . . , xn−1 satisfying the condition that if 0 < i < n, 0 < j < n, i does not equal j, and n divides (2i + j), then xi < xj. (xi denotes the ith term in the sequence of x1,x2,x3...)

Sorry, I'm not very good with Latex. Now take the sum of your answer. Now take 3072 away from your answer. Now, enter it in the answer box. Also, it would help if you proved the result you obtain, because it is pretty nice, and list all strategies you come up with for n, as many different strategies as you can, because I would like to explore deeper into this problem :). This problem is Q4 from EGMO 2014.

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