Problem 417

Let

V'(x)=\#\{\phi(m) : 1\leq m\leq x\}

and

V(x)=\#\{\phi(m) \leq x : 1\leq m\}.

Does $\lim V(x)/V'(x)$ exist? Is it $>1$ ?

Source: erdosproblems.com/417

Number theory

Wiki page

Status

Open

No claim settles this problem.

Open. The site labels the problem OPEN, and its proof-claims thread carried no claim as of 2026-10-06; no claim page is recorded: no one claims either question. Theorem 2.2 of the OpenAI release manuscript of 25 September 2026 bears on the problem without claiming it; the Current assessment records the item and why it is not a claim. The derived standing is open.

Problem 417

Status

Proof claims

Discussion