formal-conjectures · erdos-problems · ams-5
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 $\lvert A\rvert \sim N^{1/r}.$
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/30
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/241
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/241.lean
Local target: Corpus.Erdos241.erdos_241.variants.generalization
Source SHA-256: a77b5b635a57c85de04bc85c5df3474ecdac11dc2a8ea9a9d45e28880583d0e3
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
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 $\lvert A\rvert \sim N^{1/r}.$
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