Abstract:For every ǫ > 0 and k ∈ N, Haight constructed a set A ⊂ ZN (ZN stands for the integers modulo N ) for a suitable N , such that A − A = ZN and |kA|< ǫN . Recently, Nathanson posed the problem of constructing sets A ⊂ ZN for given polynomials p and q, such that p(A) = ZN and |q(A)|< ǫN , where p(A) is the set {p(a1, a2, . . . , an): a1, a2, . . . , an ∈ A}, when p has n variables. In this paper, we give a partial answer to Nathanson's question. For every k ∈ N and ǫ > 0, we find a set A ⊂ ZN for suitable N , suc… Show more
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