# Binomial Congruence

Consider the following binomial coefficient: $\dbinom{n}{\big\lceil\frac{n}{2}\big\rceil},$ where $$\lceil \cdot \rceil$$ is the ceiling function.

If it is divisible by $$n$$, what can be said about $$n \geq 2$$?

(1) Only prime odd integers work.
(2) None of the even composite integers work.
(3) All odd integers work.

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