Erdős Problem #709

Erdős problem #709 · erdosproblems.com/709

How long must an interval be to contain distinct representatives $x_i$, with $a_i \mid x_i$, for every $n$-element set of moduli $A = \{a_1, \dots, a_n\}$?

Result

Proved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Argument

Field

Extremal Divisibility

Posed by

—

Year posed

1959

Years open

67y

Solved

2026-07-13

Model

GPT-5.6 starships (Claude Fable 5 reviewer)

Vendor

OpenAI / Anthropic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article