Erdős Problem #768

Erdős problem #768 · erdosproblems.com/768

If $A(x)$ counts integers satisfying the Sylow divisor condition, determine the constant $c$ in $A(x)/x = \exp(-(c + o(1)) \sqrt{\log x} \log\log x)$. The claimed exact value is $c = 1/(2\sqrt{\log 2})$.

Result

Proved

Status

Candidate (review pending)

AI contribution

AI-discovered

Method

Argument

Field

Number Theory, Multiplicative

Posed by

—

Year posed

—

Years open

—

Solved

2026-07-25

Model

ChatGPT + Aristotle

Vendor

OpenAI / Harmonic

Collaborators

Eric Li

Verification

Lean-verified

Publication

Announced

Significance

10 / 100*

Disclosed cost

—

Wikipedia

No dedicated article