Find all natural numbers $n>3$, such that $2^{2000}$ is divisible by $1+C^1_n+C^2_n+C^3_n$.
Problem
Source: Chinese Mathematical Olympiad 1998 Problem 4
Tags: number theory unsolved, number theory
Source: Chinese Mathematical Olympiad 1998 Problem 4
Tags: number theory unsolved, number theory
Find all natural numbers $n>3$, such that $2^{2000}$ is divisible by $1+C^1_n+C^2_n+C^3_n$.