therefore
Sign up
Open navigation
All open problems
Source labels openChecked July 26, 2026

Erdős ProblemsNumber theory

Erdős Problem 830: I

Erdos Problem 830, Part 1* We say that a,b∈Na,b\in \mathbb{N} are an amicable pair if σ(a)=σ(b)=a+b\sigma(a)=\sigma(b)=a+b. Are there infinitely many amicable pairs?

Number theoryAMS 11

Mathematical statement

Erdos Problem 830, Part 1* We say that a,b∈Na,b\in \mathbb{N} are an amicable pair if σ(a)=σ(b)=a+b\sigma(a)=\sigma(b)=a+b. Are there infinitely many amicable pairs?

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_830.parts.i

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_830.parts.i : answer(sorry) ↔ {(a, b) | IsAmicable a b}.Infinite := 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 sourceformalizationerdosproblems.com/830background