Erdős Problem #942

Erdős problem #942 · erdosproblems.com/942

Let $h(n)$ count powerful integers in $[n^2, (n+1)^2)$. What is the extremal order of $h(n)$?

Result

Proved(see note)

Status

Partial result

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Powerful Numbers

Posed by

—

Year posed

1976

Years open

50y

Solved

2026-06-14

Model

Claude, Codex, Aristotle

Vendor

Anthropic / OpenAI / Harmonic

Collaborators

—

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article