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Claim. In the notation of Problem 788,

$$f(n)\ll n^{3/4}:$$

some set $B\subset(2n,4n)$ makes $|B|$ plus the largest admissible $C\subset(n,2n)$ at most a constant times $n^{3/4}$. S. L. G. Choi, On a combinatorial problem in number theory, Proc. London Math. Soc. (3) 23 (1971), no. 4, 629--642, cited as [Ch71] on the problem page. The paper is not held, and the bound is stated as the sources that cite it give it: Erdős's 1973 survey (printed p. 130) writes that "Choi conjectures $f(n)<n^{\frac12+\varepsilon}$, but can only show $f(n)<cn^{\frac34}$", and Baltz, Schoen and Srivastav (Colloq. Math. 86 (2000), p. 172) that "For an upper bound Choi proved that $f(n)=O(n^{3/4})$ and conjectured $f(n)=O(n^{1/2+\varepsilon})$". The conjecture is the problem's particular question and is not part of this claim.

Covers. The upper bound $f(n)\ll n^{3/4}$, superseded by Theorem 2 of Baltz, Schoen and Srivastav. Not covered: Choi's conjecture $f(n)\le n^{1/2+o(1)}$ and the order of growth of $f(n)$.

Depends on. No page of this wiki.

Acceptance. Refereed: the paper is the publisher's version of record in the Proceedings of the London Mathematical Society (the Crossref record gives the issue of December 1971, with no day, so this page is named by the first of the month). The site's curator, Thomas F. Bloom, credits the bound $f(n)\ll n^{3/4}$ to Choi in the problem page's commentary (label OPEN, page last edited 26 January 2026); the problem is not marked settled there, so the credit is recorded here and is not listed as reviewed. The paper itself is not held; the statement rests on the citing sources above.