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Problem 339
Let be a basis of order . Must the set of integers representable as the sum of exactly distinct elements from have positive lower density?
Source: erdosproblems.com/339
- Number theory
- Additive bases
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Solved, ProvedAn accepted solution exists. The statement is true.
The site labels the problem proved (page last edited 2025-10-14): Hegyvári, Hennecart and Plagne [HHP03] answered it, and the companion upper-density question of Erdős and Graham, in the affirmative. The accepted claim is Hegyvári, Hennecart and Plagne 2003.