We solve a problem of Filaseta by proving, that if
N is sufficiently large, A
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[
N], |
A| >
N/9 and
A + Adoes not contain any squarefree integer then all elements of A are congruent to 0 (mod 4) or 2 (mod 4). In order to show the main result we characterize the structure of all dense sets, whose elements sum to no squarefree number.