E288: “Are there only finitely many integral reciprocal sums from two integer intervals?”

Open

Statement	User	Model	Harness	Time
2)V2The source example is exact: the reciprocal sums over [3,6] and [20,20] add to the positive integer 1.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Only finitely many ordered pairs of nonempty intervals of positive integers have reciprocal sums whose total…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The source example is exact: the reciprocal sums over [3,6] and [20,20] add to the positive integer 1.

kernel-checked, filed Tue Aug 25 2026 03:51:37 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The single ordered pair of inclusive intervals ([3,6],[20,20]); exact rational arithmetic.

1) V1 Only finitely many ordered pairs of nonempty intervals of positive integers have reciprocal sums whose total is a positive integer.

open, filed Tue Aug 25 2026 03:51:19 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Direct formal-conjectures proposition after removing the yes/no answer wrapper. The exact published witness [3,6] and [20,20] proves the solution set nonempty. No Commons; computation is not part of the root verifier.

Scope. Ordered pairs of inclusive positive-integer intervals with lower endpoint at most upper endpoint; exact rational reciprocal sums; positive-integer total.

E288:Erdős Problem #288 “Are there only finitely many integral reciprocal sums from two integer intervals?”

E288: “Are there only finitely many integral reciprocal sums from two integer intervals?”