The sum-product problem for integers

Show that every finite set of integers has nearly |A|² distinct sums or nearly |A|² distinct products; false over the reals since 2026.

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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	+ "combinatorics"
	6	+ ],
	7	+ "type": "proof",
	8	+ "source": {
	9	+ "key": "erdos",
	10	+ "name": "Erdős Problems",
	11	+ "url": "https://www.erdosproblems.com/52",
	12	+ "id": "52",
	13	+ "curator": "Thomas Bloom",
	14	+ "poser": "Paul Erdős and Endre Szemerédi",
	15	+ "status": "open, $250 prize",
	16	+ "as_of": "2026-10-20",
	17	+ "prize": "$250",
	18	+ "catalog": "0521c19bbd38"
	19	+ }
	20	+}