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Very Hard

Source:

December 9, 2010
number theory unsolvednumber theory

Problem Statement

Does there exist an increasing sequence of positive integers a1,a2,⋯a_1 , a_2 ,\cdots with the following two properties?
(i) Every positive integer nn can be uniquely expressed in the form n=aj−ain = a_j - a_i ,
(ii) akk3\frac{a_k}{k^3} is bounded.
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