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Problem 6 (due Monday, April 24)

Non-negative integers di, iZ, satisfy the following condition: dk=|{i<k:di+ik}| for every integer k. Prove that there is a positive integer n such that dk{n1,n}  and  dk+n=dk for every integer k.

Only one solution was submitted, by Prof. Vladislav Kargin. His solution is different from our original solution. For details see the following link Solution.