Corpus.Erdos1.erdos_1
If $A\subseteq\{1, ..., N\}$ with $|A| = n$ is such that the subset sums $\sum_{a\in S}a$ are distinct for all $S\subseteq A$ then $$ N \gg 2 ^ n.
Erdős Problem 1
formal-conjectures · erdos-problems · ams-5 · ams-11
If $A\subseteq\{1, ..., N\}$ with $|A| = n$ is such that the subset sums $\sum_{a\in S}a$ are
distinct for all $S\subseteq A$ then
$$
N \gg 2 ^ n.
$$
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/1
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/1.lean
Local target: Corpus.Erdos1.erdos_1
Source SHA-256: c93d0da79addbacacce9b464aaa7c0a296da28261585fe8df2e0b5fdc9a3a5bf
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.
Formal targets
Reusable lemmas
No public records on this page.
Public discussion
No public records on this page.