Determine all positive integers \(n\ge 3\) such that \(2^{2000}\) is divisible by
\(1+\left(\begin{matrix}n \\ 1\end{matrix}\right)+\left(\begin{matrix}n\\ 2\end{matrix}\right)+\left(\begin{matrix}n\\ 3\end{matrix}\right)\).

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Combinatory numbers?

Latex tip for Mr.Math : \(\binom{n}{r} \)

or even
\[\dbinom{n}{k}\]

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