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Problem 849 — Erdős Problems

Problem 849

Is it true that, for every integer $t\geq 1$ , there is some integer $a$ such that

\binom{n}{k}=a

(with $1\leq k\leq n/2$ ) has exactly $t$ solutions?

Source: erdosproblems.com/849

Number theory
Binomial coefficients

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Er96b: Erdős, Paul, Some problems I presented or planned to present in my short talk. Analytic number theory, Vol. 1 (Allerton Park, IL, 1995) (1996), 333-335.
MRSTT22: Matomäki, Kaisa and Radziwiłł, Maksym and Shao, Xuancheng and Tao, Terence and Teräväinen, Joni, Singmaster's conjecture in the interior of Pascal's triangle. Q. J. Math. (2022), 1137-1177.

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Topics: Number theory
Binomial coefficients
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