Let n, k be positive integers. Prove that \(\sum_{i=1}^n k^{\gcd(i,n)}\) is divisible by n.

The best solution was submitted by Chiheon Kim(김치헌), 수리과학과 2006학번. Congratulations!

Here is his Solution of Problem 2010-4.

Alternative solutions were submitted by 정성구 (수리과학과 2007학번, +3), Prach Siriviriyakul (2009학번, +3), 라준현 (수리과학과 2008학번, +3), 서기원 (2009학번, +3), 강동엽 (2009학번, +3), 임재원 (2009학번, +2).