Monthly Archives: October 2017

Solution: 2017-15 Infinite product

For \( x \in (1, 2) \), prove that there exists a unique sequence of positive integers \( \{ x_i \} \) such that \( x_{i+1} \geq x_i^2 \) and
\[
x = \prod_{i=1}^{\infty} (1 + \frac{1}{x_i}).
\]

The best solution was submitted by Jang, Kijoung (장기정, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2017-15.

Alternative solutions were submitted by 국윤범 (수리과학과 2015학번, +3), 김기택 (수리과학과 2015학번, +3), 김태균 (수리과학과 2016학번, +3), 송교범 (고려대 수학과 2017학번, +3), 어수강 (서울대학교 수학교육과 박사과정, +3), 유찬진 (수리과학과 2015학번, +3), 윤준기 (전기및전자공학부 2014학번, +3), 이본우 (2017학번, +3), 이태영 (수리과학과 2013학번, +3), 조태혁 (수리과학과 2014학번, +3), 최대범 (수리과학과 2016학번, +3), Huy Tung Nguyen (수리과학과 2016학번, +3), 김동률 (수리과학과 2015학번, +2), 이재우 (함양고등학교 2학년, +2).

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Solution: 2017-16 Finding a rectangle

Is it possible to color all lattice points (\(\mathbb Z\times \mathbb Z\)) in the plane into two colors such that if four distinct points \( (a,b), (a+c,b), (a,b+d), (a+c,b+d)\) have the same color, then \( d/c\notin \{1,2,3,4,6\}\)?

The best solution was submitted by Choi, Daebeom (최대범, 수리과학과 2016학번). Congratulations!

Here is his solution of problem 2017-16.

Alternative solutions were submitted by 국윤범 (수리과학과 2015학번, +3), 김태균 (수리과학과 2016학번, +3), 유찬진 (수리과학과 2015학번, +3), 이수환 (수리과학과 2011학번, +3), 이재우 (함양고등학교 2학년, +3), 장기정 (수리과학과 2014학번, +3), Dung Nguyen (전산학부 2015학번, +3), Huy Tung Nguyen (수리과학과 2016학번, +3).

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