Hall's conjecture: a square extremely close to a cube

Find positive integers x, y with 0 < |y² − x³| < √x/100, beating the record ratio of about 46.6 in Hall's conjecture, unbroken since 1998.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "number-theory"
	5	+ ],
	6	+ "type": "construction",
	7	+ "source": {
	8	+ "key": "frontiermath-open",
	9	+ "name": "FrontierMath: Open Problems",
	10	+ "url": "https://epoch.ai/frontiermath/open-problems/hall-conjecture",
	11	+ "id": "hall-conjecture",
	12	+ "curator": "Epoch AI",
	13	+ "poser": "Marshall Hall Jr.",
	14	+ "status": "unsolved",
	15	+ "as_of": "2026-10-20",
	16	+ "catalog": "0521c19bbd38"
	17	+ }
	18	+}