Kurepa's conjecture

formal-conjectures · paper · ams-11

Kurepa's conjecture

For all $n$, $$!n\not\equiv 0 \mod n$$

This appears as B44 "Sums of factorials."
in Unsolved Problems in Number Theory
by *Richard K. Guy*

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A3422
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Paper/Kurepa.lean
Local target: Corpus.PaperKurepa.kurepa_conjecture
Source SHA-256: 34f3a92b793f9b3e3c6ed196325c00b8fd879bd822db5cfe5db9aed08ce7a107
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record