Mathoverflow 339137

formal-conjectures · mathoverflow · ams-12

Why do polynomials with coefficients 0,1
like to have only factors with 0,1
coefficients?

Let $P(x), Q(x) ∈ ℝ[x]$ be two monic polynomials with non-negative coefficients.
If $R(x) = P(x)Q(x)$ is a $0,1$ polynomial (coefficients only from $\{0,1\}$), then $P(x)$ and $Q(x)$
are also $0, 1$ polynomials.

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://mathoverflow.net/questions/339137
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://mathoverflow.net/users/136794/sil
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Mathoverflow/339137.lean
Local target: Corpus.Mathoverflow339137.mathoverflow_339137
Source SHA-256: 0b6f4bde28ef8e9e612570d506c8330f55ef06d0df08258be8dfd5c0b341d71c
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.

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