Find the smallest prime number \( p \geq 5 \) such that there exist no integer coefficient polynomials \( f \) and \( g \) satisfying
\[
p | ( 2^{f(n)} + 3^{g(n)})
\]
for all positive integers \( n \).

The best solution was submitted by 김태균 (수리과학과 2016학번). Congratulations!

Here is his solution of problem 2019-11.

Other solutions were submitted by 고성훈 (2018학번, +3), 조재형 (수리과학과 2016학번, +3), 채지석 (수리과학과 2016학번, +3), 최백규 (생명과학과 2016학번, +3).