Erdős Problem #320

Erdős problem #320 · erdosproblems.com/320

Let $S(N)$ count the distinct values of $\sum_{n\in A} 1/n$ over $A\subseteq\{1,\dots,N\}$. Estimate $S(N)$.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Unit Fractions

Posed by

Paul Erdős, Ronald Graham

Year posed

1980

Years open

46y

Solved

2026-07

Model

GPT-5.6 Sol

Vendor

OpenAI

Collaborators

Young, Zhu, Luo

Verification

Site-confirmed

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article