A published paper or arXiv preprint answers the main question of Erdős Problem #254 (theorem erdos_254 in formal-conjectures) in full (proof, disproof, or the exact value asked for) with no hypotheses beyond the problem's own.

The problem, as stated in formal-conjectures (Apache 2.0):

Let A\subseteq \mathbb{N} be such that \lvert A\cap [1,2x]\rvert -\lvert A\cap [1,x]\rvert \to \infty\textrm{ as }x\to \infty and \sum_{n\in A} \{ \theta n\}=\infty for every \theta\in (0,1), where \{x\} is the distance of x from the nearest integer. Then every sufficiently large integer is the sum of distinct elements of A.

References formal-conjectures lists for this problem (a starting point, not evidence):

• [Ca60] Cassels, J. W. S., On the representation of integers as the sums of distinct summands taken from a fixed set. Acta Sci. Math. (Szeged) (1960), 111-124.