Erdos's Question on Shifted Pairwise-Coprime Reciprocal Sums

Let $\mathcal{M}(n)$ be the supremum of $\sum_{a \in A} 1/(n-a)$ over pairwise coprime $A \subset [1,n)$. Erdos asked whether $\mathcal{M}(n) \le \sum_{p<n} 1/p + O(1)$ uniformly. The average order is settled: $\sum_{n \le N} \mathcal{M}(n) = e^{-\gamma} N \log\log N + O(N)$.

Result

Proved(see note)

Status

Partial result

AI contribution

AI co-developed

Method

Argument

Field

Number theory

Posed by

Paul Erdos

Year posed

—

Years open

—

Solved

2026-06-16

Model

ChatGPT

Vendor

OpenAI

Collaborators

Eric Li

Verification

Unreviewed

Publication

Preprint

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article