Prove that for all positive integers m and n, there is a positive integer k such that \[ (\sqrt{m}+\sqrt{m-1})^n = \sqrt{k}+\sqrt{k-1}.\]

The best solution was submitted by Jesek Lee (이재석), 수리과학과 2007학번. Congratulations!

Here is his Solution of Problem 2011-2.

Alternative solutions were submitted by 김인환 (2010학번, +3), 박민재 (2011학번, +3), 김지원 (2010학번, +3),강동엽 (전산학과 2009학번, +3), 서기원 (수리과학과 2009학번, +3), 김재훈 (EEWS대학원 2010학번, +3), 김현수 (한국과학영재학교 3학년, +3), 어수강 (홍익대학교 수학교육학과 2004학번, +3).