Covering systems with odd moduli

Find a finite set of congruences with distinct odd moduli that covers every integer, or prove that none exists.

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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	+ "also": [
	8	+ "proof"
	9	+ ],
	10	+ "source": {
	11	+ "key": "erdos",
	12	+ "name": "Erdős Problems",
	13	+ "url": "https://www.erdosproblems.com/7",
	14	+ "id": "7",
	15	+ "curator": "Thomas Bloom",
	16	+ "poser": "Paul Erdős and John Selfridge",
	17	+ "status": "open, $25 prize",
	18	+ "as_of": "2026-10-20",
	19	+ "prize": "$25",
	20	+ "catalog": "0521c19bbd38"
	21	+ }
	22	+}