Dense polynomials whose squares are sparse

Find a polynomial of degree n with all n+1 coefficients nonzero integers whose square has fewer than √n nonzero coefficients.

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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	+ "algebra"
	6	+ ],
	7	+ "type": "construction",
	8	+ "source": {
	9	+ "key": "frontiermath-open",
	10	+ "name": "FrontierMath: Open Problems",
	11	+ "url": "https://epoch.ai/frontiermath/open-problems/polynomial-square-few-coefficients",
	12	+ "id": "polynomial-square-few-coefficients",
	13	+ "curator": "Epoch AI",
	14	+ "status": "unsolved",
	15	+ "as_of": "2026-10-20",
	16	+ "catalog": "0521c19bbd38"
	17	+ }
	18	+}