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	"review": true,
18	"approval": "first-time"
19	}