For a positive integer \( n \), let \( d(n) \) be the number of positive divisors of \( n \). Prove that, for any positive integer \( M \), there exists a constant \( C>0 \) such that \( d(n) \geq C ( \log n )^M \) for infinitely many \( n \).

The best solution was submitted by Kim, Taegyun (김태균, 2016학번). Congratulations!

Here is his solution of problem 2016-21.

Alternative solutions were submitted by 신준형 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3, alternative solution), 국윤범 (수리과학과 2015학번, +3), 이상민 (수리과학과 2014학번, +3), 윤준기 (전기및전자공학부 2014학번, +3), 이정환 (수리과학과 2015학번, +3), Ivan Adrian Koswara (전산학부 2013학번, +3), 조준영 (수리과학과 2012학번, +3), 이시우 (포항공대 수학과 2013학번, +3).

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