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Claim. With $D(N)=\max_{1\le a<N}D(a,N)$ the least possible largest denominator in a representation of $a/N$ as a sum of distinct unit fractions, as Problem 305 defines it,

$$\frac{D(N)}{N}\le(\log N)^{1+\delta(N)},\qquad \delta(N)\to0\quad (N\to\infty).$$

This is $D(N)\ll N(\log N)^{1+o(1)}$ and answers the problem's question yes; it proves Conjecture 3 of Bleicher and Erdős (1976), of which the question is a restatement. The statement is the one the zbMATH review (Zbl 0652.10015, by Ke Zhao) gives; the paper itself is paywalled, and the explicit form $D(b)\ll b(\log b)(\log\log b)^4(\log\log\log b)^2$ is Liu and Sawhney's restatement (arXiv:2404.07113v1, p. 3). The paper closes a series of three: a reduction to prime denominators (J. Number Theory 24 (1986), 89--94), the bound $D(a,b)\le b(\log b)^{3/2}$ (J. Number Theory 28 (1988), 258--271) and this theorem, all as Liu and Sawhney recount them. The lower bound $D(p)\gg p\log p$ for primes $p$, from Bleicher and Erdős's Theorem 1 (its claim page), shows that the exponent $1$ of $\log b$ cannot be lowered.

Acceptance. Refereed: Yokota, H., On a problem of Bleicher and Erdös, J. Number Theory 30 (1988), no. 2, 198--207. The publisher's record dates the issue October 1988 and gives no day; the day in this page's name is the first of that month. Reviewed: the site's curator, Thomas Bloom, marks Problem 305 proved and credits the solution to this paper in the problem's commentary. No independent review of the proof is recorded in this corpus. The later theorem of Liu and Sawhney, on its own claim page, sharpens the bound.

Formalization. The file src/latest/ErdosProblems/Erdos305.lean in Boris Alexeev's lean-proofs collection at the pinned commit (the second link) declares itself a Lean formalization of the affirmative resolution of Problem 305, names Bleicher, Erdős, Yokota, Liu and Sawhney as its informal authors and Codex, GPT-5.6 Sol (OpenAI Codex) as its formal authors, and cites this paper's DOI among its primary references. Its theorem erdos_305 proves the problem's $b(\log b)^{1+o(1)}$ statement, not this paper's bound; its top file names the Yokota and Liu–Sawhney interval lemmas as the sharpening of a square-loss baseline without singling out either argument. The corpus did not build the file, so no formalized evidence is listed; the same link is on Liu and Sawhney's page, and the formal-conjectures statement file for the problem points at it.