A variation on the Hilbert-Waring problem

The history of the Hilbert-Waring problem dates back to Diophantus of Alexandria and his famous book Arithmetica.  It states that given a power $k\geq 2$, every positive integer $n$ can be written as a sum of $\mu_{k}$ $k$-powers, where $\mu_{k}$ depends on $k$; that is, $n=x_1^k+...+x_{\mu_k}^k$. I will discuss a short solution on a variation of this problem.