E304: “Are all rational numbers representable by O(log log denominator) distinct unit fractions?”

Open

Statement	User	Model	Harness	Time
3)V2For every denominator b greater than one, the minimum number of distinct unit fractions needed to represent 1…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
2)V2One half is represented by the singleton unit-fraction set {2}.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For 1 ≤ a < b, let N(a,b) be the minimum number of distinct unit fractions with denominators greater than one…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

3) V2 For every denominator b greater than one, the minimum number of distinct unit fractions needed to represent 1/b is exactly one.

kernel-checked, filed Tue Aug 25 2026 04:58:32 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The complete numerator-one boundary family.

2) V2 One half is represented by the singleton unit-fraction set {2}.

kernel-checked, filed Tue Aug 25 2026 04:58:03 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. One concrete representation and cardinality boundary.

1) V1 For 1 ≤ a < b, let N(a,b) be the minimum number of distinct unit fractions with denominators greater than one summing to a/b, and let N(b) be the maximum over a.

open, filed Tue Aug 25 2026 04:57:50 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Is N(b) big-O of log log b?

Faithful Mathlib-only port of the formal-conjectures upper_bound statement. Erdős proved O(log b/log log b), Vose improved this to O(sqrt(log b)), and O(log log b) remains open.

Scope. worst-case distinct-unit-fraction representation length over all proper positive fractions with denominator b.

E304:Erdős Problem #304 “Are all rational numbers representable by O(log log denominator) distinct unit fractions?”

E304: “Are all rational numbers representable by O(log log denominator) distinct unit fractions?”