Let \( n \in \mathbb{Z}^+ \) and \( x, y \in \mathbb{R}^+ \) such that \( x^n + y^n = 1 \). Prove that
\[
(1-x)(1-y) \left( \sum_{k=1}^n \frac{1+x^{2k}}{1+x^{4k}} \right) \left( \sum_{k=1}^n \frac{1+y^{2k}}{1+y^{4k}} \right) < \frac{7}{10}. \]

The best solution was submitted by 하석민 (수리과학과 2017학번). Congratulations!

Here is his solution of problem 2019-17.

Another solution was submitted by 채지석 (수리과학과 2016학번, +3).