Tag Archives: 이영민

Solution: 2019-02 Simplification of an expression with factorials

For any positive integers m and n, show that

\[ C_{n,m} = \frac{(mn)!}{(m!)^n n!} \] is an integer.

The best solution was submitted by 이영민 (수리과학과 대학원생). Congratulations!

Here is his solution of problem 2019-02.

Other solutions were submitted by Alfonso Alvarenga (전산학부 2015학번, +3), 고성훈 (2018학번, +3), 길현준 (2018학번, +3), 김기수 (수리과학과 2018학번), 김민서 (2019학번, +3), 김태균 (수리과학과 2016학번, +3), 박건규 (수리과학과 2015학번, +3), 박수찬 (전산학부 2017학번, +3), 박현영 (전기및전자공학부 2016학번, +3), 윤현민 (수리과학과 2018학번), 이본우 (수리과학과 2017학번, +3), 이상윤 (UCLA, +3), 이정환 (수리과학과 2015학번, +3), 이종서 (2019학번, +3), 이태영 (수리과학과 졸업생, +3), 조재형 (수리과학과 2016학번, +3), 조정휘 (건국대학교 수학과 2014학번, +3), 채지석 (수리과학과 2016학번, +3), 최백규 (생명과학과 2016학번, +3). Late solutions are not graded.

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Solution: 2015-10 Product of sine functions

Let \(w_1,w_2,\ldots,w_n\) be positive real numbers such that \( \sum_{i=1}^n w_i=1\). Prove that if \(x_1,x_2,\ldots,x_n\in [0,\pi]\), then \[ \sin \left(\prod_{i=1}^n x_i^{w_i} \right) \ge \prod_{i=1}^n (\sin x_i)^{w_i}.\]

The best solution was submitted by Lee, Young Min (이영민, 수리과학과 2012학번). Congratulations!

Here is his solution of problem 2015-10.

Other (but mostly identical) solutions were submitted by 고경훈 (2015학번, +3), 김기현 (수리과학과 2012학번, +3), 엄태현 (수리과학과 2012학번, +3), 오동우 (2015학번, +3), 이수철 (수리과학과 2012학번, +3), 이종원 (수리과학과 2014학번, +3), 진우영 (수리과학과 2012학번, +3), 함도규 (2015학번, +3).

 

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