# Composite numbers dividing binomial coefficients

Let $$k$$ be the number of composite integers $$n$$ that satisfy the condition that $$n$$ is a factor of $$\dbinom{n}{r}$$ for all $$r\in \{ 1, 2, 3, \ldots, n-1\}.$$ Which one of the following statements is always true for $$k$$? Prove that your answer is right.

Note: An integer number is called composite if it is greater than 1 and has at least a factor that is different from 1 and from itself.

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