Source labels openChecked July 26, 2026

Erdős Problem 850

Can there exist two distinct integers $x$ and $y$ such that $x,y$ have the same prime factors, $x+1,y+1$ have the same prime factors, and $x+2,y+2$ also have the same prime factors?

Number theory AMS 11

Mathematical statement

Can there exist two distinct integers $x$ and $y$ such that $x,y$ have the same prime factors, $x+1,y+1$ have the same prime factors, and $x+2,y+2$ also have the same prime factors?

Statement source: Erdős Problems statement material

Statement terms: Source-specific

Source-specific terms. Therefore does not assert reuse rights beyond attributed display.

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

erdos_850

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_850 :    answer(sorry) ↔ ∃ x y : ℕ, x ≠ y ∧ x.primeFactors = y.primeFactors      ∧ (x + 1).primeFactors = (y + 1).primeFactors      ∧ (x + 2).primeFactors = (y + 2).primeFactors := 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 erdosproblems.com/850background