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Erdős ProblemsCombinatorics

Erdős Problem 1: Real

A generalisation of the problem to sets A(0,N]A \subseteq (0, N] of real numbers, such that the subset sums all differ by at least 11 is proposed in [Er73] and [ErGr80].

Mathematical statement

A generalisation of the problem to sets A(0,N]A \subseteq (0, N] of real numbers, such that the subset sums all differ by at least 11 is proposed in [Er73] and [ErGr80].

[Er73] Erdős, P., Problems and results on combinatorial number theory. A survey of combinatorial theory (Proc. Internat. Sympos., Colorado State Univ., Fort Collins, Colo., 1971) (1973), 117-138.

[ErGr80] Erdős, P. and Graham, R., Old and new problems and results in combinatorial number theory. Monographies de L'Enseignement Mathematique (1980).

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_1.variants.real

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_1.variants.real :  C > (0 : ),  (N : ) (A : Finset )    (_ : IsSumDistinctRealSet A N), N  0  C * 2 ^ A.card < N := 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