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Vu, Some new results on subset sums, J. Number Theory 124 (2007), no. 1, 229–233; the Crossref record was created on 16 November 2006 (the page name's date; the record carries no online-publication date and gives the print issue as May 2007). As the site's commentary states the result, the paper improves the lower bound of Alon and Erdős for the function $f(n)$ of Problem 360 to

$$f(n)\gg\frac{n^{1/3}}{\log n},$$

removing a factor $(\log n)^{1/3}$ from the denominator of the earlier bound. The paper is not held in the library; the statement above is the site's account of it, which the introduction of Conlon, Fox and Pham (arXiv:2104.14766, Section 1.2.1, p. 5, with a sketch of Vu's argument in Section 2.3; the [[../library/integer_sequences/conlon_2021_subset_sums_completeness_colorings/_index|library card]]) confirms by citing Vu for $f(n)\ge c_1n^{1/3}/\log n$; the bibliographic data are those of the journal's Crossref record, accessed 2026-10-07.

Covers. The lower bound $f(n)\gg n^{1/3}/\log n$ only; it leaves the upper bound of Alon and Erdős in place and does not determine the order of $f$.

Accepted: the result is refereed (Journal of Number Theory). The site's commentary (erdosproblems.com/360, accessed 2026-10-07) records the bound, but its SOLVED label credits the order of growth to Conlon, Fox and Pham, so the curator's label is not review of this result. Nothing here is this project's own review.