Pollock's (tetrahedral numbers) conjecture

formal-conjectures · wikipedia · ams-11

Every positive integer is the sum of at most 5 tetrahedral numbers.

Pollock's (tetrahedral numbers) conjecture:
every integer is the sum of at most $5$ tetrahedral numbers.

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://en.wikipedia.org/wiki/Pollock%27s_conjectures
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://oeis.org/A797
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://mathworld.wolfram.com/PollocksConjecture.html
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Wikipedia/PollocksConjecture.lean
Local target: Corpus.WikipediaPollocksConjecture.pollock_tetrahedral
Source SHA-256: 2eed288143fca1a0df17021163a7a5ded59f5dfe9a96d133efc71c446fab03dd
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