Singmaster's conjecture on repeated binomial coefficients

Decide whether, for every t, some number appears as a binomial coefficient C(n,k) with k ≤ n/2 in exactly t ways.

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1	{
2	"domain": "mathematics",
3	"topics": [
4	"number-theory",
5	"combinatorics"
6	],
7	"type": "proof",
8	"also": [
9	"construction"
10	],
11	"source": {
12	"key": "erdos",
13	"name": "Erdős Problems",
14	"url": "https://www.erdosproblems.com/849",
15	"id": "849",
16	"curator": "Thomas Bloom",
17	"poser": "Paul Erdős and Basil Gordon",
18	"status": "open",
19	"as_of": "2026-10-20",
20	"catalog": "0521c19bbd38"
21	}
22	}