Claims

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1976_05_01_bleicher_erdos: Bleicher and Erdős (J. Number Theory 1976) prove D(P) >= P ceil(log_2 P) for primes P and D(N) <= K N (ln N)^3, the prime lower bound showing that the exponent 1 of log b in Problem 305 cannot be lowered; refereed.

1976_12_01_bleicher_erdos: Bleicher and Erdős (Illinois J. Math. 1976) prove D(N) <= lambda^3(N) N (ln N)^2 with lambda(N) -> 1 and sharpen their prime lower bound; the exponent 2 does not reach the 1 + o(1) of Problem 305; refereed.

1988_10_01_yokota: Yokota's 1988 theorem that D(N)/N <= (log N)^(1+delta(N)) with delta(N) -> 0 for the least largest denominator D(N), proving the Bleicher–Erdős conjecture the site credits as the solution of Problem 305; refereed.

2024_04_10_liu_sawhney: Liu and Sawhney's Theorem 1.5 (2024; IMRN 2026) that every fraction a/b is a sum of distinct unit fractions with denominators at most b(log b)(log log b)^3(log log log b)^O(1), sharpening Yokota's bound.

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