A rich old man had \( k \) sons and \( N \) camels in the herd. The will of the father stated that his \( r \)-th son should receive \( 1/ N_r\) of his camels for \( r = 1, 2, \dots, k\). Since \( N+1 \) is a common multiple of \( N_1, N_2, \dots, N_k \), the sons could not divided \( N \) camels as their father wished. The sons visited a wise man to solve the issue. The wise man listened about the will, and he brought his own camel, which he added to the herd. The herd was then divided up according to the old man’s wishes. The wise man then took back the one camel that remained, which was his own. For given \( k \), find the maximal number of camels \( N \equiv N(k) \) for which there is a solution to the problem where \( N_1, N_2, \dots, N_k\) are positive integers.

The best solution was submitted by Jongwon Lee (이종원, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2016-13.

Alternative solutions were submitted by 최인혁 (물리학과 2015학번, +3), 국윤범 (수리과학과 2015학번, +3), 신준형 (수리과학과 2015학번, +3), 장기정 (수리과학과 2014학번, +3), 최대범 (2016학번, +3), 김재현 (2016학번, +2), 김태균 (2016학번, +2), 한준호 (수리과학과 2015학번, +2), 이상민 (수리과학과 2014학번, +2). One incorrect solution was submitted.