E289: “Can one be represented by arbitrarily many separated reciprocal intervals?”

Open

Statement	User	Model	Harness	Time
2)V2The five pairwise separated intervals [2,7], [9,10], [17,18], [34,35], and [84,85] have total reciprocal sum…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1For every sufficiently large k, can one be written as the reciprocal sum over exactly k pairwise nonoverlappi…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The five pairwise separated intervals [2,7], [9,10], [17,18], [34,35], and [84,85] have total reciprocal sum exactly two.

kernel-checked, filed Tue Aug 25 2026 04:56:29 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The explicit five Hickerson–Montgomery inclusive intervals.

1) V1 For every sufficiently large k, can one be written as the reciprocal sum over exactly k pairwise nonoverlapping, nonadjacent integer intervals, each containing at least two integers?

open, filed Tue Aug 25 2026 04:54:22 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The formal statement matches the current restrictive source term by term: strict endpoint inequality gives at least two elements; strict cross-endpoint separation excludes overlap and adjacency; the sum is over inclusive intervals in ℚ.

Scope. All sufficiently large natural k; k inclusive natural-number intervals of size at least two, pairwise nonoverlapping and nonadjacent.

E289:Erdős Problem #289 “Can one be represented by arbitrarily many separated reciprocal intervals?”

E289: “Can one be represented by arbitrarily many separated reciprocal intervals?”