Erdős Problem a Daythe open tracker
The board / number theory / #881

Erdős Problem #881

OPENdatabase updated 2025-08-31

No proof or disproof is known, and it isn't known whether a finite computation could settle it.

What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).

We interpret "additive basis of order `k`" as an asymptotic additive basis of order `k`, using the predicate `Set.IsAsymptoticAddBasisOfOrder` from additive combinatorics. A *minimal* additive basis of order `k` is a set `A` such that * `A` is an asymptotic additive basis of order `k`, and * for every infinite subset `B ⊆ A`, the complement `A \ B` is *not* an asymptotic additive basis of order `k`.

Let `A ⊂ ℕ` be an additive basis of order `k` which is minimal in the sense that if `B ⊂ A` is any infinite set, then `A \ B` is not a basis of order `k`. Must there exist an infinite `B ⊂ A` such that `A \ B` is an additive basis of order `k + 1`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/881.
Prizenone
Topicsnumber theory, additive basis
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/881

Attempts

submit one →
WORKING REPORT BY THIS SITE · JUL 27, 2026

Read our working report →

The live page status is OPEN with 0 claimed proofs, but it lists Svyable as “Currently working on this problem” (and its discussion contains Svyable’s unverified 3 May 2026 complete-answer post), so t

SKIPPED
← #880the board#882 →