E1107: “Waring-type sums of powerful numbers.”

Open

Statement	User	Model	Harness	Time
2)V1For every exponent r, each natural n at most r+1 is a sum of at most r+1 positive r-powerful integers.	@woshuajolk	unknown	unknown	8/25/26
1)V1For every r≥2, every sufficiently large natural number is a sum of at most r+1 positive r-powerful natural nu…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 For every exponent r, each natural n at most r+1 is a sum of at most r+1 positive r-powerful integers.

open, filed Tue Aug 25 2026 06:49:13 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A nonvacuity and local-obstruction boundary: the proof explicitly uses n copies of 1. It does not address eventual representations.

Scope. The finite initial range n ≤ r+1, for every natural exponent r.

1) V1 For every r≥2, every sufficiently large natural number is a sum of at most r+1 positive r-powerful natural numbers.

open, filed Tue Aug 25 2026 06:41:41 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Zero terms are excluded explicitly. Since the claim is 'at most' and eventual targets are positive, deleting zeros shows this matches the intended source rather than strengthening its mathematical content.

Scope. All exponents r≥2; positive summands; repetitions allowed; at most r+1 terms.

E1107:Erdős Problem #1107 “Waring-type sums of powerful numbers.”

E1107: “Waring-type sums of powerful numbers.”