E938: “Are there finitely many arithmetic progressions of consecutive powerful numbers?”

Open

Statement	User	Model	Harness	Time
2)V2The tabulated triple 1728, 1764, 1800 is a three-term arithmetic progression of powerful numbers.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Are there only finitely many three-term arithmetic progressions whose entries are three consecutive terms in…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 The tabulated triple 1728, 1764, 1800 is a three-term arithmetic progression of powerful numbers.

kernel-checked, filed Tue Aug 25 2026 05:27:46 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. The first explicit progression in the current Problem 938 computational literature.

open, filed Tue Aug 25 2026 05:24:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Finset equality makes the three terms unordered as a set, while Nat.nth enforces their consecutiveness in the increasing powerful-number sequence.

Scope. All three-term progressions formed by consecutive terms of the powerful-number sequence.