Prove that there is a constant c>1 such that if \(n>c^k\) for positive integers n and k, then the number of distinct prime factors of \(n \choose k\) is at least k.
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2011-9 Distinct prime factors,
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Prove that there is a constant c>1 such that if \(n>c^k\) for positive integers n and k, then the number of distinct prime factors of \(n \choose k\) is at least k.
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