Source labels openChecked July 26, 2026

Erdős Problem 241: Generalization

More generally, Bose and Chowla [BoCh62] conjectured that the maximum size of $A\subseteq \{1,\ldots,N\}$ with all $r$ -fold sums distinct (aside from the trivial coincidences) then $\lvert A\rvert \sim N^{1/r}.$

Combinatorics AMS 5

Mathematical statement

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_241.variants.generalization

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_241.variants.generalization (r : ℕ) (hr : r ≥ 2) :  BoseChowlaConjecture r := 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/30background erdosproblems.com/241background