Solution: 2011-9 Distinct prime factors

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.

The best solution was submitted by Minjae Park (박민재), KAIST 2011학번. Congratulations!

Here is his Solution of Problem 2011-9.

An alternative solution was submitted by 어수강 (홍익대 수학교육과 2004학번, +3).

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1 thought on “Solution: 2011-9 Distinct prime factors

  1. 박민재

    다시 생각해보니 똑같은 논의로 k!을 lcm[1,2,…,k]으로 바꿀 수 있고, 모든 k에 대해 lcm[1,2,…,k]<=3^k가 성립하네요~

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