Source labels openChecked July 26, 2026

Numerator of a sum involving binomial coefficients

We conjecture that $u(p-1) == 0 (mod p^4)$ for all primes $p$ , with a finite number of exceptions that depend on $m$ .

Number theory AMS 11

Mathematical statement

We conjecture that $u(p-1) == 0 (mod p^4)$ for all primes $p$ , with a finite number of exceptions that depend on $m$ .

Statement source: OEIS statement material

Statement terms: CC-BY-SA-4.0

Attributed source material. Reuse must follow the linked attribution and share-alike terms.

Statement artifacts, not proofs

These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.

Pinned Lean formulation 1

general_supercongruence

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem general_supercongruence (m : ℕ) : ∃ (exceptions : Finset ℕ), ∀ p, p.Prime →    p ∉ exceptions → u m (p - 1) = (0 : ZMod (p ^ 4)) := by  sorry

Statement source: Formal Conjectures
Lean version: v4.27.0
Placeholder: Present; no proof artifact
Source evidence: Pinned source index
Fidelity review: Community formulation

References

Pinned Formal Conjectures sourceformalization A357513background