Agrawal's conjecture: Popovych
Roman B. Popovych Conjecture.* A stronger version of Agrawal's conjecture, which also considers the congruence . If both congruences hold, then is either prime or . This variant was propos...
Mathematical statement
Roman B. Popovych Conjecture.* A stronger version of Agrawal's conjecture, which also considers the congruence . If both congruences hold, then is either prime or . This variant was proposed by Roman B. Popovych in 2018.
Statement source: Wikipedia 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
agrawal_conjecture.variants.popovych
theorem agrawal_conjecture.variants.popovych : ∀ (n r : ℕ), n > 1 → r > 0 → n.gcd r = 1 → let R := Polynomial (ZMod n) let X : R := Polynomial.X let I : Ideal R := Ideal.span ({X^r - 1} : Set R) Ideal.Quotient.mk I ((X - 1)^n) = Ideal.Quotient.mk I (X^n - 1) → Ideal.Quotient.mk I ((X + 2)^n) = Ideal.Quotient.mk I (X^n + 2) → (n.Prime ∨ (n^2 : ZMod r) = 1) := 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