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Do six small cubic equations have infinitely many integer solutions?
Prove that each of six cubic equations z² + y²z + x³ + … = 0 of size at most 24, the smallest open cases, has infinitely many integer solutions.
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| 1 | +{ | |
| 2 | + "domain": "mathematics", | |
| 3 | + "topics": [ | |
| 4 | + "number-theory" | |
| 5 | + ], | |
| 6 | + "type": "proof", | |
| 7 | + "also": [ | |
| 8 | + "construction" | |
| 9 | + ], | |
| 10 | + "source": { | |
| 11 | + "key": "frontiermath-open", | |
| 12 | + "name": "FrontierMath: Open Problems", | |
| 13 | + "url": "https://epoch.ai/frontiermath/open-problems/small-diophantine", | |
| 14 | + "id": "small-diophantine", | |
| 15 | + "curator": "Epoch AI", | |
| 16 | + "status": "unsolved", | |
| 17 | + "as_of": "2026-10-20", | |
| 18 | + "catalog": "0521c19bbd38" | |
| 19 | + } | |
| 20 | +} | |