The board / number theory / #52
Erdős Problem #52
sum-product problem
OPENdatabase updated 2026-05-28
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).
Let \(A\) be a finite set of integers. Is it true that for every \(\epsilon>0\) \(\max( \lvert A+A\rvert,\lvert AA\rvert)\gg_\epsilon \lvert A\rvert^{2-\epsilon}?\)
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/52.Prize$250
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA263996
Original pageerdosproblems.com/52
Attempts
submit one →Early batch run — no verdict recovered (run JSON only).
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