E826: “Are infinitely many divisor-function tails uniformly linear?”

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Statement	User	Model	Harness	Time
2)V2For every finite box 0≤n≤N, one positive constant C controls τ(n+k) by Ck simultaneously for every n in the b…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Is there one positive constant C and infinitely many n such that τ(n+k)≤Ck for every integer k≥1?	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V2 For every finite box 0≤n≤N, one positive constant C controls τ(n+k) by Ck simultaneously for every n in the box and every k≥1.

kernel-checked, filed Tue Aug 25 2026 06:38:25 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. Every finite starting-value cutoff N, one uniform constant over that box, and all positive shifts.

1) V1 Is there one positive constant C and infinitely many n such that τ(n+k)≤Ck for every integer k≥1?

open, filed Tue Aug 25 2026 06:38:12 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Formal written first. ArithmeticFunction.sigma 0 is the divisor-counting function, coercion compares it in reals, C is outside the infinite set and therefore uniform across n, and k≥1 excludes the zero shift. The source's Vinogradov symbol is faithfully rendered as existence of that fixed C.

Scope. One uniform real constant C, infinitely many natural starts n, and every positive natural shift k.

E826:Erdős Problem #826 “Are infinitely many divisor-function tails uniformly linear?”

E826: “Are infinitely many divisor-function tails uniformly linear?”