Let \( n \) be a positive integer. Suppose that \( a_1, a_2, \dots, a_n \) are non-zero integers and \( b_1, b_2, \dots, b_n\) are positive integers such that \( (b_i, b_n) = 1 \) for \( i = 1, 2, \dots, n-1 \). Prove that the Diophantine equation
\[
a_1 x_1^{b_1} + a_2 x_2^{b_2} + \dots + a_n x_n^{b_n} = 0
\]
has infinitely many integer solutions \( (x_1, x_2, \dots, x_n) \).

The best solution was submitted by Chae, Jiseok (채지석, 수리과학과 2016학번). Congratulations!

Here is his solution of problem 2018-15.

An alternative solution was submitted by Saba Dzmanashvili (수리과학과 2017학번, +3), 강한필 (전산학부 2016학번, +3), 권홍 (중앙대 물리학과, +3), 이본우 (수리과학과 2017학번, +3), 이재우 (함양고등학교 3학년, +3), 최백규 (생명과학과 2016학번, +3), 길현준 (2018학번, +2), 김태균 (수리과학과 2016학번, +2).