Prove that each positive integer x can be written as a sum of at most 53 integers to the fourth power. In other words, for every positive integer x, there exist \(y_1,y_2,\ldots,y_k\) with \(k\le 53\) such that \(x=\sum_{i=1}^k y_i^4\).

The best solution was submitted by SangHoon Kwon (권상훈), 수리과학과 2006학번.

Here is his Solution of Problem 2009-6.

There were 4 other submitted solutions: 백형렬, 이재송, 조강진, 김치헌 (+3).