# 2009-6 Sum of integers of the fourth power

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 $$x=\sum_{i=1}^k y_i^4$$.

GD Star Rating