Arbitrarily long runs of equal signs of the Liouville function

Prove that the Liouville function takes the same sign on arbitrarily long blocks of consecutive integers.

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	1	+{
	2	+ "domain": "mathematics",
	3	+ "topics": [
	4	+ "number-theory"
	5	+ ],
	6	+ "type": "proof",
	7	+ "source": {
	8	+ "key": "aimpl",
	9	+ "name": "AIM Problem Lists",
	10	+ "url": "http://aimpl.org/sarnakconjecture/2/",
	11	+ "id": "sarnakconjecture 2.2",
	12	+ "curator": "American Institute of Mathematics",
	13	+ "status": "open",
	14	+ "as_of": "2026-10-20",
	15	+ "catalog": "0521c19bbd38"
	16	+ }
	17	+}