Erdős Problem #633
SOLVEDdatabase updated 2026-04-06
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A triangle is `n`-cuttable if it can be decomposed into `n` congruent triangles.
A triangle whose side lengths and angles are integrally independent is cuttable only into a non-zero square number of congruent triangles. This is proved in [So09c].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 3 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/633.Prize$25
Topicsgeometry
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/633
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.